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A TOPOLOGISED MEASURE HOMOLOGY

Published online by Cambridge University Press:  01 September 2008

RICARDO BERLANGA
RICARDO BERLANGA*
Affiliation:
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS), Departamento de Métodos Matemáticos y NuméricosUniversidad Nacional Autónoma de México (UNAM)04510 Mexico D.F., Mexico e-mail: [email protected]
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Abstract

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A homology theory based on measures, first mentioned by Thurston, is naturally defined here as a functor into the category of locally convex topological vector spaces. It is proved that the first homology space is Hausdorff.

Keywords

55N35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 359 - 369
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Benedetti, R. and Petronio, C., Lectures on hyperbolic geometry, Universitext (Springer-Verlag, Berlin, 1992).CrossRefGoogle Scholar
2.Biss, D. K., The topological fundamental group and generalized covering spaces, Topol. Appl. 3 (124) (2002), 355–371.CrossRefGoogle Scholar
3.Dugundji, J., Topology (Allyn and Bacon, Inc., Boston, 1970).Google Scholar
4.Dugundji, J., A topologized fundamental group, Proc. Nat. Acad. Sci. U.S.A. 2 (36) (1950), 141–143.CrossRefGoogle Scholar
5.Fabel, P., The topological hawaiian earring group does not embed in the inverse limit of free groups, Algebr. Geom. Topol. 5 (2005), 1585–1587.CrossRefGoogle Scholar
6.Fabel, P., The fundamental group of the harmonic archipelago, arXiv:math/0501426v1.Google Scholar
7.Fabel, P., Topological fundamental groups can distinguish spaces with isomorphic homotopy groups, Topol. Proc. 1 (30) (2006), 187–195.Google Scholar
8.Fabel, P., Metric spaces with discrete topological fundamental group, Topol. Appl. 154 (2007), 635–638.CrossRefGoogle Scholar
9.Fathi, A., Structure of the group of homeomorphisms preserving a good measure, Ann. Sci. École Norm. Sup. 13 (4) (1980), 45–93.CrossRefGoogle Scholar
10.Gromov, M., Volume and bounded cohomology, Pub. Math. IHES 56 (1982), 5–99.Google Scholar
11.Hansen, S. K., Measure homology, Math. Scand. 83 (1998), 205–219.CrossRefGoogle Scholar
12.Hilton, P. J. and Stammbach, U., A course in homological algebra, Grad. Texts in Math. 4 (Springer-Verlag, Berlin, 1971).CrossRefGoogle Scholar
13.Kuessner, T., Efficient fundamental cycles of cusped hyperbolic manifolds, Pacific J. Math. 2 (211) (2003), 283–313.CrossRefGoogle Scholar
14.Löh, C., Measure homology and singular homology are isometrically isomorphic, Math. Z. 1 (253) (2006), 197–218.CrossRefGoogle Scholar
15.Milnor, J., On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959), 272–280.Google Scholar
16.Munkholm, H. J., Simplices of maximal volume in hyperbolic space, Gromov's norm, and Gromov's proof of Mostow's rigidity theorem (following Thurston), in: Topology symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), Lect. Notes in Math. 788 (Springer-Verlag, Berlin, 1980).CrossRefGoogle Scholar
17.Ratcliffe, J. G., Foundations of hyperbolic manifolds, Grad. Texts in Math. 149 (Springer-Verlag, Berlin, 1994).CrossRefGoogle Scholar
18.Royden, H. L., Real analysis, 2nd ed. (The Macmillan Company, London, 1968).Google Scholar
19.Rudin, W., Functional analysis (McGraw-Hill, New York, 1973).Google Scholar
20.Rudin, W., Real and complex analysis, 2nd ed. (McGraw-Hill, New York, 1974).Google Scholar
21.Soma, T., Degree-one maps between hyperbolic 3-manifolds with the same volume limit, Trans. Amer. Math. Soc. 7 (353) (2001), 2753–2772.CrossRefGoogle Scholar
22.Spanier, E. H., Algebraic topology (McGraw-Hill, New York, 1966).Google Scholar
23.Thurston, W. P., The geometry and topology of three-manifolds, circulated lecture notes, Princeton University 1979, now also electronically available at http://www.msri.org/publications/books/gt3m/Google Scholar
24.Willard, S., General topology (Addison-Wesley Publishing Company, Reading, MA, 1970).Google Scholar
25.Whitehead, G. W., Elements of homotopy theory, Grad. Texts in Math. 61 (Springer-Verlag, Berlin, 1978).Google Scholar
26.Whitehead, J. H. C., Combinatorial homotopy I. Bull. Amer. Math. Soc. 55 (1949), 213–245.CrossRefGoogle Scholar
27.Zastrow, A., On the (non)-coincidence of Milnor–Thurston homology theory with singular homology theory, Pacific J. Math. 2 (186) (1998), 369–396.CrossRefGoogle Scholar