Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-15T11:14:33.938Z Has data issue: false hasContentIssue false
  • English
  • Français

The ER(z)-cohomology of Bℤ/(2q) and ℂℙn

Published online by Cambridge University Press:  20 November 2018

Nitu Kitchloo ,
Vitaly Lorman  and
W. Stephen Wilson
Nitu Kitchloo
Affiliation:
Department of Mathematics, Johns Hopkins University, Baltimore, USA e-mail: [email protected], [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The $ER\left( 2 \right)$-cohomology of $B\mathbb{Z}/\left( {{2}^{q}} \right)$ and $\mathbb{C}{{\mathbb{P}}^{n}}$ are computed along with the Atiyah–Hirzebruch spectral sequence for $ER{{\left( 2 \right)}^{*}}\left( \mathbb{C}{{\mathbb{P}}^{\infty }} \right)$. This, along with other papers in this series, gives us the $ER\left( 2 \right)$-cohomology of all Eilenberg–MacLane spaces.

Keywords

55N2055N9155P2055T25complex projective spacecohomology theoryEilenberg–MacLane spaceAtiyah–Hirzebruch spectral sequence
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 1 , 01 February 2018 , pp. 191 - 217
Copyright
Copyright © Canadian Mathematical Society 2018

References

[Ban13] Banerjee, R., On the ER(2)-cohomology of some odd-dimensional projective spaces. Topology Appl. 160(2013), 1395–1405.http://dx.doi.Org/10.1016/j.topol.2013.05.017 Google Scholar
[HK01] Hu, P. and Kriz, I., Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence. Topology 40(2001), 317–399.http://dx.doi.org/10.1016/S0040-9383(99)00065-8 Google Scholar
[HM16] Hill, M. A. and Meier, L., The C2-spectrum TMF and its invertible modules. arxiv:1 507.08115v3 Google Scholar
[JW73] Johnson, D. C. and Wilson, W. S., Projective dimension and Brown-Peterson homology. Topology 12(1973), 327–353.http://dx.doi.org/10.1016/0040-9383(73)90027-X Google Scholar
[KLW16] Kitchloo, N., Lorman, V., and Wilson, W. S., Landweber flat real pairs, and ER(n)-cohomology. 2016. arxiv:1 603.06865 Google Scholar
[KW07a] Kitchloo, N. and Wilson, W. S., On fibrations related to real spectra. In: Proceedings of the Nishida Fest (Kinosaki 2003), Geom. Topol. Monogr., 10, Geom. Topol. Publ., Coventry, 2007, pp. 237–244. http://dx.doi.org/10.2140/gtm.2007.10.237 Google Scholar
[KW07b] Kitchloo, N. and Wilson, W. S., On the Hopf ring for ER(n). Topology Appl. 154(2007), 1608–1640.http://dx.doi.org/10.1016/j.topol.2007.01.001 Google Scholar
[KW08a] Kitchloo, N. and Wilson, W. S., The second real Johnson-Wilson theory and non-immersions of RPn. Homology Homotopy Appl. 10(2008), 223–268. http://dx.doi.org/10.4310/HHA.2008.v10.n3.a11 Google Scholar
[KW08b] Kitchloo, N. and Wilson, W. S., The second real Johnson-Wilson theory and non-immersions of RPn. II. Homology Homotopy Appl. 10(2008), 269–290.http://dx.doi.org/10.4310/HHA.2008.v10.n3.a12 Google Scholar
[KW13] Kitchloo, N. and Wilson, W. S., Unstable splittings for real spectra. Algebr. Geom. Topol. 13(2013), 1053–1070.http://dx.doi.Org/10.214O/agt.2O13.13.1053 Google Scholar
[KW15] Kitchloo, N. and Wilson, W. S., The ER(n)-cohomology of BO(q) and real Johnson-Wilson orientations for vector bundles. Bull. Lond. Math. Soc. 47(2015), 835–847.http://dx.doi.Org/10.1112/blms/bdvO57 Google Scholar
[Lan70] Landweber, P. S., Coherence, flatness and cobordism of classifying spaces. In: Proceedings of Advanced Study Institute on Algebraic Topology, Mat. Inst., Aarhus, 1970, pp. 256–269.Google Scholar
[Lor16] Lorman, V., The real Johnson-Wilson cohomology ℂℙ∞. Topology Appl. 209(2016), 367–388.http://dx.doi.org/10.1016/j.topol.2016.06.018 Google Scholar