Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T02:46:25.525Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  15 June 2021

Michael A. Hill ,
Michael J. Hopkins  and
Douglas C. Ravenel
Michael A. Hill
Affiliation:
University of California, Los Angeles
Michael J. Hopkins
Affiliation:
Harvard University, Massachusetts
Douglas C. Ravenel
Affiliation:
University of Rochester, New York
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem , pp. 830 - 841
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adámek, Jiří, Herrlich, Horst, and Strecker, George E. (1990). Abstract and concrete categories: the joy of cats. John Wiley & Sons, Inc., New York. 2.3CGoogle Scholar
Adámek, J., Rosický, J., and Vitale, E. M. (2010). What are sifted colimits? Theory Appl. Categ., 23:No. 13, 251–260. 2.3.74, 2.3GGoogle Scholar
Adámek, J., Rosický, J., and Vitale, E. M. (2011). Algebraic theories, volume 184 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge. 2.3G, 2.3GGoogle Scholar
Adams, J. F. (1958). On the structure and applications of the Steenrod algebra. Comment. Math. Helv., 32:180–214. 1.1, 1.2CCrossRefGoogle Scholar
Adams, J. F. (1960). On the non-existence of elements of Hopf invariant one. Ann. Math. (2), 72:20–104. 1.2C, 1.2.5CrossRefGoogle Scholar
Adams, J. F. (1962). Vector fields on spheres. Ann. Math. (2), 75:603–632. 1.2DCrossRefGoogle Scholar
Adams, J. F. (1964). Stable homotopy theory, volume 3 of Lecture Notes in Math. Springer-Verlag, Berlin. 1.3A, (ii), 5.7BGoogle Scholar
Adams, J. F. (1966). On the groups J(X). IV. Topology, 5:21–71. 1.2.2CrossRefGoogle Scholar
Adams, J. F. (1974a). Operations of the nth kind in K-theory, and what we don’t know about RP 8 . In New developments in topology (Proc. Sympos. Algebraic Topology, Oxford, 1972), pages 1–9, volume 11 of London Math. Soc. Lecture Note Ser., Cambridge University Press, London. 9.1.44Google Scholar
Adams, J. F. (1974). Stable homotopy and generalised homology. University of Chicago Press, Chicago, Chicago Lectures in Mathematics. 1.3B, 1.3B, 5.7B, 5.7B, 7, 7.0A, 7.0A, (i), 7.2.41, 8.0BGoogle Scholar
Adams, J. F. (1980). Graeme Segal’s Burnside ring conjecture. In Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), volume 788 of Lecture Notes in Math., pages 378–395. Springer, Berlin. 9.1.44CrossRefGoogle Scholar
Adams, J. F. (1984). Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture. In Algebraic topology, Aarhus 1982 (Aarhus, 1982), volume 1051 of Lecture Notes in Math., pages 483–532. Springer, Berlin. 8.0A, 9.4B, 9.5CrossRefGoogle Scholar
Alexander, J. W. II. (1915). A proof of the invariance of certain constants of analysis situs. Trans. Amer. Math. Soc., 16(2):148–154. 8.0BCrossRefGoogle Scholar
Angeltveit, Vigleik. (2008). Enriched Reedy categories. Proc. Amer. Math. Soc., 136(7): 2323–2332. 5.5.10CrossRefGoogle Scholar
Antolin-Camarena, Omar. (2014). The nine model category structures on the category of sets. www.matem.unam.mx/omar/notes/modelcatsets.html. 4.1BGoogle Scholar
Antolin-Camarena, Omar, and Barthel, Tobias. (2014). Chromatic fracture cubes. https://arxiv.org/abs/1410.7271. 2.3EGoogle Scholar
Araki, Shôrô. (1979). Orientations in τ-cohomology theories. Japan. J. Math. (N.S.), 5(2):403–430. 1.1B, (ii), 12.2B, 12.2.10, 12.2.13, 12.2B, 12.2.24CrossRefGoogle Scholar
Arf, Cahit. (1941). Untersuchungen über quadratische Formen in Körpern der Charakteris-tik 2. I. J. Reine Angew. Math., 183:148–167. 1.2CCrossRefGoogle Scholar
Atiyah, M. F. (1961). Thom complexes. Proc. London Math. Soc. (3), 11:291–310. 8.0BCrossRefGoogle Scholar
Atiyah, M. F. (1966). K-theory and reality. Quart. J. Math. Oxford Ser. (2), 17:367–386. 1.1B, 13.3BCrossRefGoogle Scholar
Ayala, David, and Francis, John. (2019). A factorization homology primer. https://arxiv.org/abs/1903.10961. 2.4Google Scholar
Barratt, M. G., and Milnor, John. (1962). An example of anomalous singular homology. Proc. Amer. Math. Soc., 13:293–297. 3.5.31CrossRefGoogle Scholar
Barratt, M. G., Mahowald, M. E., and Tangora, M. C. (1970). Some differentials in the Adams spectral sequence. II. Topology, 9:309–316. 1.2CCrossRefGoogle Scholar
Barratt, M. G., Jones, J. D. S., and Mahowald, M. E. (1984). Relations amongst Toda brackets and the Kervaire invariant in dimension 62. J. London Math. Soc. (2), 30(3):533–550. 1.1, 1.2CCrossRefGoogle Scholar
Barthel, Tobias, and Riehl, Emily. (2013). On the construction of functorial factorizations for model categories. Algebr. Geom. Topol., 13(2):1089–1124. 4.2A, 5.2.17CrossRefGoogle Scholar
Barwick, Clark. (2010). On left and right model categories and left and right Bousfield localizations. Homology, Homotopy Appl., 12(2):245–320. 6.3, 6.3A, 6.3ACrossRefGoogle Scholar
Barwick, Clark. (2017). Spectral Mackey functors and equivariant algebraic K-theory (I). Adv. Math., 304:646–727. 8.2BGoogle Scholar
Batanin, M. A., and Berger, C. (2017). Homotopy theory for algebras over polynomial monads. Theory Appl. Categ., 32:Paper No. 6, 148–253. 5.1.18Google Scholar
Bayeh, Marzieh, Hess, Kathryn, Karpova, Varvara, et al. (2015). Left-induced model structures and diagram categories. In Women in topology: collaborations in homotopy theory, volume 641 of Contemp. Math., pages 49–81. Amer. Math. Soc., Providence, RI. 5.2ACrossRefGoogle Scholar
Barthel, Tobias and Beaudry, Agnes. Chromatic structures in stable homotopy theory. In Miller, Haynes R., editor, Handbook of homotopy theory, CRC Press/Chapman and Hall Handbooks in Mathematics Series, pages 163–220. CRC Press, Boca Raton, FL, 2020. https://arxiv.org/abs/1901.09004. 1.1ACrossRefGoogle Scholar
Beke, Tibor. (2000). Sheafifiable homotopy model categories. Math. Proc. Cambridge Philos. Soc., 129(3):447–475. 6.3ACrossRefGoogle Scholar
Blanc, David. (1996). New model categories from old. J. Pure Appl. Algebra, 109(1): 37–60. 5.2B, 5.2BGoogle Scholar
Blumberg, Andrew J., and Mandell, Michael A. (2015). The homotopy theory of cyclo-tomic spectra. Geom. Topol., 19(6):3105–3147. 9.11C, 9.11.48CrossRefGoogle Scholar
Boardman, J. M., and Vogt, R. M. (1973). Homotopy invariant algebraic structures on topological spaces, volume 347 of Lecture Notes in Math. Springer-Verlag, Berlin-New York. 1.3ACrossRefGoogle Scholar
Bohmann, Anna Marie. (2014). A comparison of norm maps. Proc. Amer. Math. Soc., 142(4):1413–1423. 9.7CCrossRefGoogle Scholar
Borceux, Francis. (1994). Basic category theory. Handbook of categorical algebra. 1, volume 50 of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge. 2.7, 2.7.5Google Scholar
Borceux, Francis. (1994). Categories and structures. Handbook of categorical algebra. 2, volume 51 of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge. 2.8, 3.1B, (iii)Google Scholar
Bott, Raoul. (1959). The stable homotopy of the classical groups. Ann. Math. (2), 70: 313–337. 1.2.2CrossRefGoogle Scholar
Bousfield, A. K. (1975). The localization of spaces with respect to homology. Topology, 14:133–150. (i), 6, 6.1, 6.1A, 6.2, 6.2ACrossRefGoogle Scholar
Bousfield, A. K. (1979). The localization of spectra with respect to homology. Topology, 18(4):257–281. (i), 6.1BCrossRefGoogle Scholar
Bousfield, A. K. (2001). On the telescopic homotopy theory of spaces. Trans. Amer. Math. Soc., 353(6):2391–2426. 5.3, 6.2BCrossRefGoogle Scholar
Bousfield, A. K. (1976–1977). Constructions of factorization systems in categories. J. Pure Appl. Algebra, 9(2):207–220. 2.3B, 4.8CrossRefGoogle Scholar
Bousfield, A. K., and Friedlander, E. M. (1978). Homotopy theory of Ɣ-spaces, spectra, and bisimplicial sets. In Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, volume 658 of Lecture Notes in Math., pages 80–130. Springer, Berlin. 1.4C, 1.4D, 5, 5.8.41, 6.1, 6.1C, 7.0A, (i), (i), 7.0C, 7.3.8, 7.3ACrossRefGoogle Scholar
Bousfield, A. K., and Kan, D. M. (1972). Homotopy limits, completions and localizations, 304 of Lecture Notes in Math. Springer-Verlag, Berlin-New York. 1.3, 1.4, 3, 3.4A, 3.4.14, 5, 5.4A, 5.8, 5.8A, 5.8A, 5.8A, 5.8.5, 6CrossRefGoogle Scholar
Bredon., Glen E. (1967). Equivariant cohomology theories, volume 34 of Lecture Notes in Math. Springer-Verlag, Berlin and New York. Definition 8.4.4, 8.4, 8.8CrossRefGoogle Scholar
Bredon, Glen E. (1993). Topology and geometry, volume 139 of Graduate Texts in Mathematics. Springer-Verlag, New York. 3.5ACrossRefGoogle Scholar
Browder, William. (1969). The Kervaire invariant of framed manifolds and its generalization. Ann. Math. (2), 90:157–186. 1.1, 1.2CCrossRefGoogle Scholar
Brown, Edgar H. Jr. (1962). Cohomology theories. Ann. Math. (2), 75:467–484. 7.2CCrossRefGoogle Scholar
Brown, Edgar H. Jr., and Peterson, Franklin P. (1966). The Kervaire invariant of (8k + 2)-manifolds. Amer. J. Math., 88:815–826. 1.2CCrossRefGoogle Scholar
Brown, Ronald. (1987). From groups to groupoids: a brief survey. Bull. London Math. Soc., 19(2):113–134. 2.1ECrossRefGoogle Scholar
Brown, Ronald. (2006). Topology and groupoids. BookSurge, LLC, Charleston, SC. 2.1E, 2.1E, 2.1E, 2.1E, 2.1.35, 2.1EGoogle Scholar
Brun, Morten, Dundas, Bjørn Ian, and Stolz, Martin. (2016). Equivariant structure on smash powers. http://arxiv.org/abs/1604.05939. 2.6.35, 2.6D, 2.6G, 2.6G, (ii), 5.6B, 5.6B, 8.0D, 8.6, 8.6.1, 8.6B, 9.1EGoogle Scholar
Burnside, William. (1911) Theory of groups of finite order. Cambridge University Press, Cambridge. 8.1, 8.1, 8.1, 8.1.6Google Scholar
Carlsson, Gunnar. (1984). Equivariant stable homotopy and Segal’s Burnside ring conjecture. Ann. of Math. (2), 120(2):189–224. 9.11BCrossRefGoogle Scholar
Casacuberta, Carles, and Frei, Armin. (2000). On saturated classes of morphisms. Theory Appl. Categ., 7(4): 43–46. 4.8Google Scholar
Cheng, Eugenia, and Lauda, Aaron. (2004). Higher-dimensional categories: an illustrated guide book, Note. 2.7Google Scholar
Cohen, Joel M. (1970). Stable homotopy, volume 165 of Lecture Notes in Math. Springer-Verlag, Berlin-New York. 1.1, 1.2.5Google Scholar
Crans, Sjoerd E. (1995). Quillen closed model structures for sheaves. J. Pure Appl. Algebra, 101(1):35–57. 5.2BCrossRefGoogle Scholar
Cruttwell, G. S. H. (2008). Normed spaces and the change of base for enriched categories. Thesis, Dalhousie University. 3.1B, 3.1BGoogle Scholar
Day, Brian. (1970). On closed categories of functors. In Reports of the Midwest Category Seminar, IV, volume 137 of Lecture Notes in Math., pages 1–38. Springer, Berlin. 1.3B, 1.4B, 3.3Google Scholar
Dold, Albrecht, and Puppe, Dieter. (1980). Duality, trace, and transfer. In Proceedings of the International Conference on Geometric Topology (Warsaw, 1978), pages 81–102. PWN, Warsaw. 8.0BGoogle Scholar
Dress, Andreas. (1969). A characterisation of solvable groups. Math. Z., 110:213–217. 8.1, 8.1Google Scholar
Dress, Andreas W. M. (1973). Contributions to the theory of induced representations. In Algebraic K-theory, II: “classical” algebraic K-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), volume 342 in Lecture Notes in Math., pages 183–240. Springer, Berlin. 8.2AGoogle Scholar
Dugger, Daniel. (2001). Replacing model categories with simplicial ones. Trans. Amer. Math. Soc., 353(12):5003–5027 (electronic). 4.5CrossRefGoogle Scholar
Dugger, Daniel. (2006). Spectral enrichments of model categories. Homology Homotopy Appl., 8(1):1–30. 3.1.7CrossRefGoogle Scholar
Dugger, Daniel. (2017). A primer on homotopy colimits. http://pages.uoregon.edu/ddugger/hocolim.pdf. 2.3H, 5.8, 5.8D, 5.8D, 5.8DGoogle Scholar
Dugger, Daniel, and Isaksen, Daniel C. (2004). Topological hypercovers and A1 -realizations. Math. Z., 246(4):667–689. 5.8BCrossRefGoogle Scholar
Dundas, Bjørn Ian, Röndigs, Oliver, and Østvær, Paul Arne. (2003). Enriched functors and stable homotopy theory. Doc. Math., 8:409–488. 7.0A, 7.0F, (i), (iii), (iv), 7.1.5, 7.1.16, 7.2, 7.2A, 7.2A, 7.2.25, 7.2B, 7.2BCrossRefGoogle Scholar
Dwyer, William G., Hirschhorn, Philip S., and Kan, Daniel M. (1997). Model categories and more general abstract homotopy theory: a work in what we like to think of as progress. Preprint, MIT. 2.3B, 5.2A, 5.2A, 5.2A, 5.2B, 5.2BGoogle Scholar
Dwyer, William G., Hirschhorn, Philip S., Kan, Daniel M., and Smith, Jeffrey H. (2004). Homotopy limit functors on model categories and homotopical categories, volume 113 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI. 4.3, 4.8, 5, 5.1, 5.1A, 5.1A, 5.1A, 5.1B, 5.2AGoogle Scholar
Dwyer, W. G., and Kan, D. M. (1980). Function complexes in homotopical algebra. Topology, 19(4):427–440. 4.6Google Scholar
Dwyer, W. G., and Kan, D. M. (1984). A classification theorem for diagrams of simplicial sets. Topology, 23(2):139–155. 5Google Scholar
Dwyer, W. G., and Kan, D. M. (1985). Equivariant homotopy classification. J. Pure Appl. Algebra, 35(3):269–285. 5CrossRefGoogle Scholar
Dwyer, W. G., and Spaliński, J. (1995). Homotopy theories and model categories. In Handbook of algebraic topology, pages 73–126. North-Holland, Amsterdam. 1.4C, 4, 4.2A, 4.2C, 4.4, 4.4, 4.5CrossRefGoogle Scholar
Eda, Katsuya, and Kawamura, Kazuhiro. (2000a). Homotopy and homology groups of the n-dimensional Hawaiian earring. Fund. Math., 165(1):17–28. 3.5.31CrossRefGoogle Scholar
Eda, Katsuya, and Kawamura, Kazuhiro. (2000b). The singular homology of the Hawaiian earring. J. London Math. Soc. (2), 62(1):305–310. 3.5.31Google Scholar
Eilenberg, Samuel, and Kelly, G. Max. (1966). Closed categories. In Proc. Conf. Categorical Algebra (La Jolla, CA, 1965), pages 421–562. Springer, New York. 1.3B, 2.7, 3.1, 3.1BGoogle Scholar
Eilenberg, Samuel, and Mac Lane, Saunders. (1945). General theory of natural equivalences. Trans. Amer. Math. Soc., 58:231–294. 2Google Scholar
Eilenberg, Samuel, and Moore, John C. (1965). Adjoint functors and triples. Illinois J. Math., 9:381–398. 2, 2.2ECrossRefGoogle Scholar
El Bashir, Robert, and Velebil, Jiří. (2002). Simultaneously reflective and coreflective subcategories of presheaves. Theory Appl. Categ., 10:No. 16, 410–423. 2.2.53Google Scholar
Elmendorf, A. D. (1983). Systems of fixed point sets. Trans. Amer. Math. Soc., 277(1): 275–284. 8.8, 8.8.1CrossRefGoogle Scholar
Elmendorf, A. D. Kriz, I., Mandell, M. A., and May, J. P. (1997). Rings, modules, and algebras in stable homotopy theory, volume 47 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI. 1.3B, 1.4B, 3.5.22, 5.6A, 7.0B, 13.3BGoogle Scholar
Farjoun, E. Dror. (1996a). Cellular spaces, null spaces and homotopy localization, volume 1622 of Lecture Notes in Math. Springer-Verlag, New York. (ii), 6.2ACrossRefGoogle Scholar
Farjoun, E. Dror. (1996b). Higher homotopies of natural constructions. J. Pure Appl. Algebra, 108(1):23–34. 6.2ACrossRefGoogle Scholar
Freudenthal, H. (1938). Über die Klassen der Sphärenabbildungen I. Grosse Dimensionen Compositio Math., 5:299–314. 1.2A, 1.3Google Scholar
Fujii, Michikazu. (1975/1976). Cobordism theory with reality. Math. J. Okayama Univ., 18(2):171–188. 1.1B, (ii)Google Scholar
Gabriel, Peter, and Ulmer, Friedrich. (1971). Lokal präsentierbare Kategorien, volume 221 of Lecture Notes in Math. Springer-Verlag, Berlin-New York. 2.3GCrossRefGoogle Scholar
Garner, Richard. (2009). Understanding the small object argument. Appl. Categ. Structures, 17(3):247–285. 4.8CrossRefGoogle Scholar
Goerss, Paul G., and Jardine, John F. (1999). Simplicial homotopy theory, volume 174 of Progress in Mathematics. Birkhäuser Verlag, Basel. 3.4, 3.4BGoogle Scholar
Goerss, P. G., and Hopkins, M. J. (2004). Moduli spaces of commutative ring spectra. In Structured ring spectra, volume 315 of London Math. Soc. Lecture Note Ser., pages 151–200. Cambridge University Press, Cambridge. 1.1ACrossRefGoogle Scholar
Greenlees, J. P. C. (1992). Some remarks on projective Mackey functors. J. Pure Appl. Algebra, 81(1):17–38. 8.2CGoogle Scholar
Greenlees, J. P. C., and May, J. P. (1995). Equivariant stable homotopy theory. In Handbook of algebraic topology, pages 277–323. North-Holland, Amsterdam. 1, 8, 8.0ACrossRefGoogle Scholar
Greenlees, J. P. C., and May, J. P. (1997). Localization and completion theorems for MU-module spectra. Ann. of Math. (2), 146(3):509–544. 9.7CGoogle Scholar
Guillou, Bertrand, May, J. P., and Rubin, Jonathan. (2010). Enriched model categories in equivariant contexts. http://arxiv.org/abs/1307.4488. 8.6BGoogle Scholar
Guillou, Bertrand, and May, J. P. (2011). Enriched model categories and presheaf categories. http://arxiv.org/abs/1110.3567. 2.6D, 5.4A, 5.6AGoogle Scholar
Guillou, Bertrand, and Yarnall, Carolyn. (2018). The Klein four slices of positive suspensions of HF2. http://arxiv.org/abs/1808.05547. 11.2.13Google Scholar
Hahn, Jeremy, and Shi, XiaoLin Danny. Real orientations of Morava E-theories. https://arxiv.org/abs/1707.03413. 1.1BGoogle Scholar
Hatcher, Allen. (2002). Algebraic topology. Cambridge University Press, Cambridge. 5.6AGoogle Scholar
Hazewinkel, Michiel. (1978). Formal groups and applications, volume 78 of Pure and Applied Mathematics. Academic Press Inc. New York. 13.4B, 13.4BGoogle Scholar
Hazewinkel, M., editor. (2000). Encyclopaedia of mathematics. Supplement. Vol. II. Kluwer Academic Publishers, Dordrecht. 2.7CrossRefGoogle Scholar
Heller, Alex. (1988). Homotopy theories. Mem. Amer. Math. Soc., 71(383):vi+78. 5.4AGoogle Scholar
Hess, Kathryn, Kȩdziorek, Magdalena, Riehl, Emily, and Shipley, Brooke. (2017). A necessary and sufficient condition for induced model structures. J. Topol., 10(2): 324–369. 5.2B, 5.2B, 5.2BCrossRefGoogle Scholar
Higgins, Philip J. (1971). Notes on categories and groupoids. Van Nostrand Reinhold Co., London-New York-Melbourne. Van Nostrand Rienhold Mathematical Studies, No. 32. 2.1EGoogle Scholar
Hill, Michael A. (2012). The equivariant slice filtration: a primer. Homology Homotopy Appl., 14(2):143–166. 11.1.14, 11.2.13CrossRefGoogle Scholar
Hill, M. A., and Hopkins, M. J. (2014). Equivariant multiplicative closure. In Algebraic topology: applications and new directions, volume 620 of Contemp. Math., pages 183–199. Amer. Math. Soc., Providence, RI. 13.3BGoogle Scholar
Hill, M. A., and Hopkins, M. J. (2016). Equivariant symmetric monoidal structures. https://arxiv.org/abs/1610.03114. 13.3BGoogle Scholar
Hill, M. A., Hopkins, M. J., and Ravenel, D. C. (2016). On the nonexistence of elements of Kervaire invariant one. Ann. of Math. (2), 184(1):1–262. 1, 1.1A, 1.1C, 1.3, 1.4, 1.4C, 2, 2.9, 2.9.3, 3.1.59, 5, 5.1, 5.1C, 7.0C, 8.0D, 8.3B, 8.6.19, 8.9.10, 8.9.40, 9.0.2, 9.2, 9.2, 11, 11.1.5, 11.1.6, 11.1.11, 11.1.14, 11.3.6, 11.3.14, 11.3, 11.4.7, 13.4Google Scholar
Hill, Michael A., Hopkins, M. J., and Ravenel, D. C. (2017a). The slice spectral sequence for certain RO(Cpn)-graded suspensions of HZ. Bol. Soc. Mat. Mex. (3), 23(1):289–317, 2017. 9.9, 9.9Google Scholar
Hill, Michael A., Hopkins, M. J., and Ravenel, Douglas C. (2017b). The slice spectral sequence for the C4 analog of real K-theory. Forum Math., 29(2):383–447. 1.1B, 1.1CGoogle Scholar
Hill, Michael A., and Yarnall, Carolyn. (2018). A new formulation of the equivariant slice filtration with applications to Cp-slices. Proc. Amer. Math. Soc., 146(8):3605–3614. 11, 11.1D, 11.2.13Google Scholar
Hirschhorn, Philip S. (2003). Model categories and their localizations, volume 99 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI. 1.3, 1.4, 2.2C, 2.3A, 2.3B, 2.6.15, 3.1.57, 3.4.2, 3.4.5, 3.4.14, 3.4B, 4, 4.1C, 4.1.24, 4.1C, 4.1C, 4.3, 4.3, 4.3, 4.4, 4.4, 4.5, 4.5, 4.5, 4.8, 4.8, 4.8, 4.8, 4.8, 5.1A, 5.2A, 5.2A, 5.2B, 5.2B, 5.3, 5.3, 5.4A, 5.4B, 5.4B, 5.6A, 5.6A, 5.6A, 5.6.23, 5.8, 5.8A, 5.8B, 5.8E, 5.8F, 5.8F, 5.8F, 5.8F, 5.8F, 6, 6.2A, 6.2.2, 6.2A, 6.2A, 6.2A, 6.2A, 6.3, 6.3A, 6.3A, 6.3B, 6.3B, 6.3B, 6.3C, 7.1.34, 7.3.8Google Scholar
Hirschhorn, Philip S. (2015). Overcategories and undercategories of model categories. https://arxiv.org/abs/1507.01624. 4.1.14 Google Scholar
Hopf, H. (1935). Über die Abbildungen von Spha¨ren auf Sphären niedrigerer Dimension. Fundamenta Mathematica, 25:427–440. 1.2.2CrossRefGoogle Scholar
Hovey, Mark. (1998). Monoidal model categories. https://arxiv.org/abs/math/9803002. 5.5CGoogle Scholar
Hovey, Mark. (1999). Model categories, volume 63 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI. 2.1F, 2.1F, 2.3B, 2.3G, 2.6.18, 2.6C, 2.6D, 2.7, (iv), (v), (v), (ii), 4, 4.1D, 4.2A, 4.2D, 4.3, 4.3, 4.3, 4.4.9, 4.5, 4.5, 4.5, 4.6, 4.7, 4.8, 4.8, 5, 5.1A, 5.2B, 5.5A, 5.5A, 5.5A, 5.5A, 5.5.11, 5.5B, 5.5B, 5.5.20, 5.5D, 5.5D, 5.7Google Scholar
Hovey, Mark. (2001a). Errata to model categories. http://hopf.math.purdue.edu/Hovey/model-err.pdf. 2.3GGoogle Scholar
Hovey, Mark. (2001b). Spectra and symmetric spectra in general model categories. J. Pure Appl. Algebra, 165(1):63–127. 5.2A, 5.6A, 5.6.23, 5.8E, 6.3A, 6.3A, 7.0A, (i), 7.0F, (iv), 7.1.4, 7.1.16, 7.1.20, 7.1.24, 7.1, 7.1, 7.1, 7.1.34, 7.1, 7.3.8, 7.3A, 7.3C, 7.3E, 7.4BGoogle Scholar
Hovey, Mark. (2014). Smith ideals of structured ring spectra. http://arxiv.org/abs/1401.2850. 5.5D, 5.5DGoogle Scholar
Hovey, Mark, Shipley, Brooke, and Smith, Jeff. (2000). Symmetric spectra. J. Amer. Math. Soc., 13(1):149–208. 1.3B, 1.4B, 1.4D, 2.3B, 2.3.16, 3.1E, 7.0B, 7.0E, 7.0E, 7.0F, (iv), 7.1.20, 7.1.24, 7.2, 7.2B, 7.2C, 7.3, 7.3DCrossRefGoogle Scholar
Hoyois, Marc. (2015). From algebraic cobordism to motivic cohomology, note. 11Google Scholar
Hu, Po, and Kris, Igor. (2001). Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence. Topology, 40(2):317–399. 1.1B, (ii), 12.2B, 12.2B, 12.2B, 12.4A, 13.3A, 13.3.11Google Scholar
Illman, Sören. (1978). Smooth equivariant triangulations of G-manifolds for G a finite group. Math. Ann., 233(3):199–220. 10.5Google Scholar
Illman, Sören. (1983). The equivariant triangulation theorem for actions of compact Lie groups. Math. Ann., 262(4):487–501. 10.5Google Scholar
Isaken, Daniel C. (2004). Strict model structures for pro-categories. In Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001), volume 215 of Progr. Math., pages 179–198. Birkhäuser, Basel. 5.2AGoogle Scholar
James, I. M. (1955). Reduced product spaces. Ann. Math. (2), 62:170–197. 1.2DCrossRefGoogle Scholar
James, I. M. (1956a). On the suspension triad. Ann. Math. (2), 63:191–247. 1.2DGoogle Scholar
James, I. M. (1956b). The suspension triad of a sphere. Ann. of Math. (2), 63:407–429. 1.2DCrossRefGoogle Scholar
James, I. M. (1957). On the suspension sequence. Ann. Math. (2), 65:74–107. 1.2DCrossRefGoogle Scholar
James, I. M. editor. Handbook of algebraic topology. North-Holland, Amsterdam, 1995. 1.4CGoogle Scholar
Janelidze, G., and Kelly, G. M. (2001/2002). A note on actions of a monoidal category. Theory Appl. Categ., 9:61–91. CT2000 Conference (Como). 2.6BGoogle Scholar
Jones, John D. S. (1978). The Kervaire invariant of extended power manifolds. Topology, 17(3):249–266. 1.2CGoogle Scholar
Joyal, A. (2002). Quasi-categories and Kan complexes. J. Pure Appl. Algebra, 175(1-3): 207–222. Special volume celebrating the 70th birthday of Professor Max Kelly. 2.7, 4.2.19CrossRefGoogle Scholar
Joyal, André, and Tierney, Myles. (2007). Quasi-categories vs Segal spaces. In Categories in algebra, geometry and mathematical physics, volume 431 of Contemp. Math., pages 277–326. Amer. Math. Soc., Providence, RI. 2.3B, 4.1ACrossRefGoogle Scholar
Kan, Daniel M. (1958a). Adjoint functors. Trans. Amer. Math. Soc., 87:294–329. 1.3B, 1.4A, 2, 2.2D, (ii), 2.3C, 2.6C, 3.4ACrossRefGoogle Scholar
Kan, Daniel M. (1958b). On homotopy theory and c.s.s. groups. Ann. Math. (2), 68:38–53. 4CrossRefGoogle Scholar
Kashiwara, Masaki, and Schapira, Pierre. (2006). Categories and sheaves, volume 332 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin. 2.3HCrossRefGoogle Scholar
Kelly, Gregory Maxwell. (1982). Basic concepts of enriched category theory, volume 64 of London Math. Soc. Lecture Note Ser. Cambridge University Press, Cambridge. 1.3B, 2.2E, 2.5B, 2.6.35, 2.8, 3, 3.1, 3.1A, 3.1B, 3.1B, 3.1.27, 3.1B, 3.1B, 3.1.30, 3.2A, 3.2B, 3.2C, 3.2.19, 3.2C, 3.2DGoogle Scholar
Kervaire, Michel A. (1960). A manifold which does not admit any differentiable structure. Comment. Math. Helv., 34:257–270. 1.2C, 1.2CCrossRefGoogle Scholar
Kinoshita, Yoshkiki. (1996). Prof. Nobuo Yoneda passed away. www.mta.ca/„cat-dist/catlist/1999/yoneda. 2Google Scholar
Kochman, Stanley O. (1978). A chain functor for bordism. Trans. Amer. Math. Soc., 239:167–196. 13.1.4CrossRefGoogle Scholar
Kochman, Stanley O. (1980). Uniqueness of Massey products on the stable homotopy of spheres. Canad. J. Math., 32(3):576–589. 13.1.4Google Scholar
Kochman, Stanley O. (1982). The symplectic cobordism ring. II. Mem. Amer. Math. Soc., 40(271):vii+170. 13.1.4Google Scholar
Landweber, Peter S. (1968). Conjugations on complex manifolds and equivariant homotopy of MU. Bull. Amer. Math. Soc., 74:271–274. 1.1B, (ii)CrossRefGoogle Scholar
Lang, Serge. (1965). Algebra. Addison-Wesley Publishing Co., Inc., Reading, Mass. 8.1Google Scholar
Laplaza, Miguel L. (1972). Coherence for distributivity. In Coherence in categories, pages 29–65, volume 281 of Lecture Notes in Math. Springer, Berlin. 2.9BCrossRefGoogle Scholar
Lawvere, F. W. (1994). Cohesive toposes and Cantor’s “lauter Einsen”. Philos. Math. (3), 2(1):5–15. Categories in the foundations of mathematics and language. 2.2.53CrossRefGoogle Scholar
Leinster, Tom. (2004). Higher operads, higher categories, volume 298 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge. 2.7, 2.7, 2.7.5, 2.8.8Google Scholar
Levine, Marc. (2013). Convergence of Voevodsky’s slice tower. Doc. Math., 18:907–941. 11CrossRefGoogle Scholar
Lewis, L. Gaunce Jr. (1980). The theory of Green functors. Mimeographed notes, University of Chicago. 8.2BGoogle Scholar
Lewis, L. Gaunce Jr. (1988). The RO(G)-graded equivariant ordinary cohomology of complex projective spaces with linear Zp actions. In Algebraic topology and transformation groups (Göttingen, 1987), volume 1361 of Lecture Notes in Math., pages 53–122. Springer, Berlin. 8.2DCrossRefGoogle Scholar
Lewis, L. G. Jr., May, J. P., Steinberger, M., and McClure, J. E. (1986). Equivariant stable homotopy theory, volume 1213 of Lecture Notes in Math. Springer-Verlag, Berlin. With contributions by J. E. McClure. 1, 2.6E, 2.6E, 3.5A, 5.7B, 7.0A, (i), 8.0C, 9.11.1, 11.3.11Google Scholar
Li, Guchuan, Shi, XiaoLin Danny, Wang, Guozhen, and Xu, Zhouli. (2019). Hurewicz images of real bordism theory and real Johnson–Wilson theories. Adv. Math., 342: 67–115. 13.1CrossRefGoogle Scholar
Lima, Elon L. (1959). The Spanier–Whitehead duality in new homotopy categories. Summa Brasil. Math., 4:91–148. 1.3, 7.0AGoogle Scholar
Lindner, Harald. (1976). A remark on Mackey-functors. Manuscripta Math., 18(3): 273–278. 8.2BGoogle Scholar
Lin, Wen-Hsiung. (1979) The Adams–Mahowald conjecture on real projective spaces. Math. Proc. Cambridge Philos. Soc., 86(2):237–241. 9.1.44Google Scholar
Lin, W. H., Davis, D. M., Mahowald, M. E., and Adams, J. F. (1980). Calculation of Lin’s Ext groups. Math. Proc. Cambridge Philos. Soc., 87(3):459–469. 9.1.44CrossRefGoogle Scholar
Lind, John A. (2013). Diagram spaces, diagram spectra and spectra of units. Algebr. Geom. Topol., 13(4):1857–1935. 2.3DCrossRefGoogle Scholar
Lubin, Jonathan, and Tate, John. (1965). Formal complex multiplication in local fields. Ann. Math. (2), 81:380–387. 13.4BCrossRefGoogle Scholar
Lück, Wolfgang. (2005). Survey on classifying spaces for families of subgroups. In Infinite groups: geometric, combinatorial and dynamical aspects, volume 248 of Progr. Math., pages 269–322. Birkhäuser, Basel. 8.6ACrossRefGoogle Scholar
Lurie, Jacob. (2009). Higher topos theory, volume 170 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ. 1.4A, 2.4, 2.7, 4.2.19, 4.4, 4.8, 4.8, (i), 5.5.11, 5.8, 6.3, 6.3AGoogle Scholar
Lurie, Jacob. (2010). Chromatic homotopy theory, lecture series 2010. www.math.ias.edu/„lurie/252x.html. 1.1AGoogle Scholar
Lurie, Jacob. (2017). Higher algebra. www.math.ias.edu/„lurie/papers/HA.pdf. 2.5AGoogle Scholar
Lydakis, Manos. (1998). Simplicial functors and stable homotopy theory. Preprint 98-049, SFB 343, Bielefeld. 7.0A, 7.0F, (iii), 7.2Google Scholar
Mac Lane, Saunders. (1971). Categories for the working mathematician. Springer-Verlag, New York, volume 5 of Graduate Texts in Mathematics. Springer-Verlag, New York. 1.4A, 2.2E, 2.4CrossRefGoogle Scholar
Mac Lane, Saunders. (1998). Categories for the working mathematician, volume 5 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2nd edition. 2, 2.2A, 2.2D, 2.2D, 2.2E, 2.2E, 2.3C, 2.3C, 2.3G, 2.3H, 2.3H, 2.4, 2.5, 2.5A, 2.5B, 2.6A, 2.6G, 2.6.58Google Scholar
Mac Lane, Saunders, and Moerdijk, Ieke. (1994). Sheaves in geometry and logic. Univer-sitext. Springer-Verlag, New York. 2.2EGoogle Scholar
Mahowald, Mark. (1967). The metastable homotopy of Sn. Memoirs of the American Mathematical Society, No. 72. American Mathematical Society, Providence, RI. 1.2DGoogle Scholar
Mahowald, Mark. (1977). A new infinite family in 2π˚s. Topology, 16(3):249–256. 1.2.5CrossRefGoogle Scholar
Mahowald, Mark. (1982). The image of J in the EHP sequence. Ann. Math. (2), 116(1):65–112. 1.2DCrossRefGoogle Scholar
Mahowald, Mark, and Tangora, Martin. (1967). Some differentials in the Adams spectral sequence. Topology, 6:349–369. 1.2CCrossRefGoogle Scholar
Mandell, M. A., and May, J. P. (2002). Equivariant orthogonal spectra and S-modules. Mem. Amer. Math. Soc., 159(755):x+108. 1.3B, (i), 1.4D, 5.4A, 7.2, 8.0D, 8.6, 8.6, 8.6B, 8.6B, 8.9C, 9, 9.0.2, 9.1.8, 9.2, 9.3, 9.4A, 9.8, 9.11C, 9.11C, 9.11E, 9.11.47, 9.11.49, 10.5, 10.8A, 10.8A, 12.1Google Scholar
Mandell, M. A., May, J. P., Schwede, S., and Shipley, B. (2001). Model categories of diagram spectra. Proc. London Math. Soc. (3), 82(2):441–512. 1.3B, (ii), 1.4B, 1.4D, 2.2C, 2.3.16, 2.5B, 3.1E, 3.3, 3.5.22, 5.2A, 5.4A, 5.4.22, 5.5.28, 5.6A, (i), 7.2, 7.2.34, 7.2B, 7.2C, 7.3A, 7.4, 8.6B, 9.2, 9.4ACrossRefGoogle Scholar
May, J. Peter. (1967). Simplicial objects in algebraic topology. Van Nostrand Mathematical Studies, No. 11. D. Van Nostrand Co., Inc., Princeton, NJ-Toronto, ON-London. 3.4AGoogle Scholar
May, J. P. (1996). Equivariant homotopy and cohomology theory, volume 91 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC. With contributions by Cole, M., Comezaña, G., Costenoble, S., Elmendorf, A. D., Greenlees, J. P. C., Lewis, L. G. Jr., Piacenza, R. J., Triantafillou, G., and Waner, S.. 2, 8.3.15Google Scholar
May, J. P. (1999a). A concise course in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL. 3.5A, 3.5AGoogle Scholar
May, J. P. (1999b). The hare and the tortoise. In Homotopy invariant algebraic structures (Baltimore, MD, 1998), volume 239 of Contemp. Math., pages 9–13. Amer. Math. Soc., Providence, RI. 1.3AGoogle Scholar
May, J. P., and Ponto, K. (2012). More concise algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL. Localization, completion, and model categories. 1.4C, 2.3B, 2.3B, 4, 4.8, 4.8, 5.2BGoogle Scholar
Mazure, Kristen. (2015). An equivariant tensor product on Mackey functors. https://arxiv.org/abs/1508.04062. 8.2EGoogle Scholar
McCord, M. C. (1969). Classifying spaces and infinite symmetric products. Trans. Amer. Math. Soc., 146:273–298. 2.1F, 2.1.47CrossRefGoogle Scholar
Miller, Haynes. (2017). The Burnside bicategory of groupoids. Bol. Soc. Mat. Mex. (3), 23(1):173–194. 2.1EGoogle Scholar
Miller, Haynes R. (1984). The Sullivan conjecture on maps from classifying spaces. Ann. Math. (2), 120(1):39–87. (i)CrossRefGoogle Scholar
Miller, Haynes R., Ravenel, Douglas C., and Wilson, W. Stephen. (1977). Periodic phenomena in the Adams–Novikov spectral sequence. Ann. Math. (2), 106(3): 469–516. 1.1ACrossRefGoogle Scholar
Milnor, John. (1956). Construction of universal bundles. II. Ann. of Math. (2), 63:430–436. 3.4.17Google Scholar
Milnor, J. (1960). On the cobordism ring ˚ and a complex analogue. I. Amer. J. Math., 82:505–521. 12, 12.3ACrossRefGoogle Scholar
Milnor, John W., and Stasheff, James D. (1974). Characteristic classes, vol. 76 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ. 1.2A, 1.2.2, (iv), (iv)CrossRefGoogle Scholar
Minami, Norihiko. (1965). The Adams spectral sequence and the triple transfer. Amer. J. Math., 117(4):965–985. 1.2.5Google Scholar
Munson, Brian, and Volic, Ismar. (2015). Cubical homotopy theory, volume 25 of New Mathematical Monographs. Cambridge University Press, Cambridge. 2.3ECrossRefGoogle Scholar
Pontryagin, L. S. (1938). A classification of continuous transformations of a complex into a sphere, 1 and 2. Doklady Akad. Nauk SSSR (N.S.), 19:147–149 and 361–363. 1.2AGoogle Scholar
Pontryagin, L. S. (1950). Homotopy classification of the mappings of an (n + 2)-dimensional sphere on an n-dimensional one. Doklady Akad. Nauk SSSR (N.S.), 70:957–959. 1.2A, 1.2A, 1.2CGoogle Scholar
Pontryagin, L. S. (1955). Gladkie mnogoobraziya i ih primeneniya v teorii gomotopiĭ [Smooth manifolds and their applications in homotopy theory]. Trudy Mat. Inst. im. Steklov. No. 45. Izdat. Akad. Nauk SSSR, Moscow. 1.2A, 1.2AGoogle Scholar
Quillen, Daniel G. (1967). Homotopical algebra, volume 43 of Lecture Notes in Math. Springer-Verlag, Berlin-New York. 1.4C, 1.4C, 2.3.16, 4, 4.1.6, 4.2, 4.2B, 4.2D, 4.3, (i), 4.3, 4.3, 4.3, 4.5, 4.6, 4.6, 4.6, 4.7, 4.7, 4.7, 4.8, 5.6AGoogle Scholar
Quillen, Daniel. (1969a). On the formal group laws of unoriented and complex cobordism theory. Bull. Amer. Math. Soc., 75:1293–1298. 12.2CCrossRefGoogle Scholar
Quillen, Daniel. (1969b). Rational homotopy theory. Ann. Math. (2), 90:205–295. 5Google Scholar
Quillen, Daniel. (1970). On the (co-) homology of commutative rings. In Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968), pages 65–87. Amer. Math. Soc., Providence, RI. 1.4C, 5Google Scholar
Quillen, D. G. (1971). Elementary proofs of some results of cobordism theory using Steenrod operations. Adv. Math., 7:29–56. 12.2CCrossRefGoogle Scholar
Raptis, George. (2010). Homotopy theory of posets. Homology Homotopy Appl., 12(2):211–230. 5.2.17Google Scholar
Ravenel, Douglas C. (1978). The non-existence of odd primary Arf invariant elements in stable homotopy. Math. Proc. Cambridge Philos. Soc., 83(3):429–443. 1.1ACrossRefGoogle Scholar
Ravenel, Douglas C. (1984). Localization with respect to certain periodic homology theories. Amer. J. Math., 106(2):351–414. 1.4C, (i)CrossRefGoogle Scholar
Ravenel, Douglas C. (1986). Complex cobordism and stable homotopy groups of spheres, volume 121 of Pure and Applied Mathematics. Academic Press Inc., Orlando, FL. 1.5Google Scholar
Ravenel, Douglas C. (1992). Nilpotence and periodicity in stable homotopy theory, volume 128 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ. Appendix C by Jeff Smith. 1.1A, 1.3, 1.4, 1.4C, (i)Google Scholar
Ravenel, Douglas C. (2004). Complex cobordism and stable homotopy groups of spheres, Second Edition. American Mathematical Society, Providence, RI. 1.1, 1.1A, 1.2C, 1.2D, 1.3, 1.4, 2.1.18, 12, 13.1.4, 13.4A, 13.4A, 13.4C, 13.4C, 13.4CGoogle Scholar
Rezk, Charles. (1998). Notes on the Hopkins-Miller theorem. In Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997), volume 220 of Contemp. Math., pages 313–366. Amer. Math. Soc., Providence, RI. 1.1AGoogle Scholar
Riehl, Emily. (2014). Categorical homotopy theory, volume 24 of New Mathematical Monographs. Cambridge University Press, Cambridge. 2, 2.1F, 2.3B, 2.5A, 2.6D, 2.8, 3.1A, 3.1B, 3.2, 3.2C, 4.1B, 4.4, 4.8, 5.1, 5.1A, 5.1B, 5.8, 5.8A, 5.8CCrossRefGoogle Scholar
Riehl, Emily. (2017). Category theory in context. Aurora: Modern Math Originals. Dover Publications. 2.2D, 2.2E, 2.3CGoogle Scholar
Schwede, Stefan. (2007). An untitled book project about symmetric spectra. www.math.uni-bonn.de/people/schwede/. 7.0E, 7.0F, (iv), 12Google Scholar
Schwede, Stefan. (2014). Lectures on equivariant stable homotopy theory. www.math.uni-bonn.de/people/schwede/. 9.1E, 9.3, 9.10, 11.3.11Google Scholar
Schwede, Stefan, and Shipley, Brooke E. (2000). Algebras and modules in monoidal model categories. Proc. London Math. Soc. (3), 80(2):491–511. 2.3B, 4.8, 5, 5.2B, 5.5C, 5.5C, 5.5C, 5.5.28, 5.5D, 10.7, 10.8A, 10.8ACrossRefGoogle Scholar
Schwede, Stefan, and Shipley, Brooke. (2003a). Equivalences of monoidal model categories. Algebr. Geom. Topol., 3:287–334 (electronic). 5.5B, 9.11.31Google Scholar
Schwede, Stefan, and Shipley, Brooke E. (2003b). Stable model categories are categories of modules. Topology, 42(1):103–153. 5.7Google Scholar
Segal, G. B. (1971). Equivariant stable homotopy theory. In Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pages 59–63. Gauthier-Villars, Paris. 1Google Scholar
Segal, Graeme. (1968). Classifying spaces and spectral sequences. Inst. Hautes Études Sci. Publ. Math., (34):105–112. 3.4.17Google Scholar
Serre, Jean-Pierre. (1967). Représentations linéaires des groupes finis. Hermann, Paris. 8.2AGoogle Scholar
Shimomura, Katsumi. (1981). Novikov’s Ext2 at the prime 2. Hiroshima Math. J., 11(3):499–513. 13.4AGoogle Scholar
Shulman, Michael. (2006). Homotopy limits and colimits and enriched homotopy theory. http://arxiv.org/abs/math/0610194. 2.6C, 2.6D, 2.6D, 4.4, 5.1, 5.1A, 5.8Google Scholar
Snaith, Victor P. (2009). Stable homotopy around the Arf–Kervaire invariant, volume 273 of Progress in Mathematics. Birkhäuser Verlag, Basel. 1.1Google Scholar
Spanier, E. H. (1959). Function spaces and duality. Ann. Math. (2), 70:338–378. 7.0A, 8.0BCrossRefGoogle Scholar
Spanier, E. H., and Whitehead, J. H. C. (1955). Duality in homotopy theory. Mathematika, 2:56–80. 8.0BGoogle Scholar
Stephan, Marc. (2016). On equivariant homotopy theory for model categories. Homology Homotopy Appl., 18(2):183–208. 8.6BGoogle Scholar
Stong, Robert E. (1968a). Notes on Cobordism Theory. Princeton University Press, Princeton, NJ. 1.2A, 12.2CGoogle Scholar
Strøm, Arne. (1972). The homotopy category is a homotopy category. Arch. Math. (Basel), 23:435–441. 4.2A, 5.2.17, 5.8BGoogle Scholar
Strickland, Neil P. (2009). The category of cgwh spaces. http://neil-strickland.staff.shef.ac.uk/courses/homotopy/. 2.1F, 2.1.47Google Scholar
Sullivan, Dennis. (1971). Geometric topology. Part I. Massachusetts Institute of Technology, Cambridge, MA. (i)Google Scholar
Tamaki, D. (2009). The Grothendieck construction and gradings for enriched categories. https://arxiv.org/abs/0907.0061. 2.8Google Scholar
tom Dieck, Tammo. (1975). Orbittypen und äquivariante Homologie. II. Arch. Math. (Basel), 26(6):650–662. 9.11.1Google Scholar
tom Dieck, Tammo. (1979). Transformation groups and representation theory, volume 766 of Lecture Notes in Math. Springer, Berlin. 8.1, 11.3.11Google Scholar
Thévenaz, Jacques, and Webb, Peter J. (1989). Simple Mackey functors. In Proceedings of the Second International Group Theory Conference (Bressanone, 1989), number 23, pages 299–319. 8.2CGoogle Scholar
Thévenaz, Jacques, and Webb, Peter. (1995). The structure of Mackey functors. Trans. Amer. Math. Soc., 347(6):1865–1961. (ii), 8.2CCrossRefGoogle Scholar
Thom, René. (1954). Quelques propriétés globales des variétés différentiables. Comment. Math. Helv., 28:17–86. 1.2A, 12.2CGoogle Scholar
Toda, Hirosi. (1967). An important relation in homotopy groups of spheres. Proc. Japan Acad., 43:839–842. 1.1AGoogle Scholar
Toda, Hirosi. (1968). Extended p-th powers of complexes and applications to homotopy theory. Proc. Japan Acad., 44:198–203. 1.1AGoogle Scholar
Toda, Hirosi. (1971). On spectra realizing exterior parts of the Steenrod algebra. Topology, 10:53–65. (ii)CrossRefGoogle Scholar
Ullman, John. (2013). On the slice spectral sequence. Algebr. Geom. Topol., 13(3):1743–1755. 11.1.5, 11.1.14CrossRefGoogle Scholar
Vistoli, Angelo. (2005). Grothendieck topologies, fibered categories and descent theory. In Fundamental algebraic geometry, volume 123 of Math. Surveys Monogr., pages 1–104. Amer. Math. Soc., Providence, RI. 2.8Google Scholar
Voevodsky, Vladimir. (2002). Open problems in the motivic stable homotopy theory. I. In Motives, polylogarithms and Hodge theory, part I (Irvine, CA, 1998), volume 3 of Int. Press Lect. Ser., pages 3–34. Int. Press, Somerville, MA. 11Google Scholar
Voevodsky, V. (2004). On the zero slice of the sphere spectrum. Tr. Mat. Inst. Steklova, 246 (Algebr. Geom. Metody, Svyazi i Prilozh.):106–115. 11Google Scholar
White, David. (2018). Monoidal Bousfield localizations and algebras over operads. http://arxiv.org/abs/1404.5197. 6.2D, 6.2DGoogle Scholar
White, David. (2017). Model structures on commutative monoids in general model categories. J. Pure Appl. Algebra, 221(12):3124–3168. 5.5C, 5.5CGoogle Scholar
Whitehead, George W. (1942). On the homotopy groups of spheres and rotation groups. Ann. Math. (2), 43:634–640. 1.2.2Google Scholar
Whitehead, George W. (1950). The (n + 2)nd homotopy group of the n-sphere. Ann. Math. (2), 52:245–247. 1.2AGoogle Scholar
Whitehead, George W. (1962). Generalized homology theories. Trans. Amer. Math. Soc., 102:227–283. 7.0ACrossRefGoogle Scholar
Wirthmüller, Klaus. (1974). Equivariant homology and duality. Manuscripta Math., 11:373–390. 8.0DGoogle Scholar
Xu, Zhouli. (2016). The strong Kervaire invariant problem in dimension 62. Geom. Topol., 20(3):1611–1624. 1.1, 1.2CGoogle Scholar
Yarnall, Carolyn. (2017) The slices of Sn ^ HZ for cyclic p-groups. Homology Homotopy Appl., 19(1):1–22, 2017. 11.2.13CrossRefGoogle Scholar
Yoneda, Nobuo. (1954). On the homology theory of modules. J. Fac. Sci. Univ. Tokyo. Sect. I., 7:193–227. 2Google Scholar
Yoneda, Nobuo. (1960). On Ext and exact sequences. J. Fac. Sci. Univ. Tokyo Sect. I, 8: 507–576 (1960). 2.4Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Michael A. Hill, University of California, Los Angeles, Michael J. Hopkins, Harvard University, Massachusetts, Douglas C. Ravenel, University of Rochester, New York
  • Book: Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem
  • Online publication: 15 June 2021
  • Chapter DOI: https://doi.org/10.1017/9781108917278.017
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Michael A. Hill, University of California, Los Angeles, Michael J. Hopkins, Harvard University, Massachusetts, Douglas C. Ravenel, University of Rochester, New York
  • Book: Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem
  • Online publication: 15 June 2021
  • Chapter DOI: https://doi.org/10.1017/9781108917278.017
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Michael A. Hill, University of California, Los Angeles, Michael J. Hopkins, Harvard University, Massachusetts, Douglas C. Ravenel, University of Rochester, New York
  • Book: Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem
  • Online publication: 15 June 2021
  • Chapter DOI: https://doi.org/10.1017/9781108917278.017
Available formats
×