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Homotopy Equivalence and Groups of Measure-Preserving Homeomorphisms

Published online by Cambridge University Press:  20 November 2018

R. Berlanga
R. Berlanga*
Affiliation:
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 04510 México D.F., México e-mail: [email protected]
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Abstract

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It is shown that the group of compactly supported, measure-preserving homeomorphisms of a connected, second countable manifold is locally contractible in the direct limit topology. Furthermore, this group is weakly homotopically equivalent to the more general group of compactly supported homeomorphisms.

Keywords

57S0558F11
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 3 , 01 September 2006 , pp. 337 - 346
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Berlanga, R., A mapping theorem for topological sigma-compact manifolds. Compositio Math. 63(1987), no. 2, 209–216.Google Scholar
[2] Berlanga, R., Groups of measure-preserving homeomorphisms as deformation retracts. J. London Math. Soc. 68(2003), no. 1, 241–254.Google Scholar
[3] Berlanga, R. and Epstein, D. B. A., Measures on sigma-compact manifolds and their equivalence under homeomorphism. J. London Math. Soc. 27(1983), no. 1, 63–74.Google Scholar
[4] černavskii, A. V., Local contractibility of the group of homeomorphisms of a manifold. Soviet Math. Dokl. 9(1968), 1171–1174.Google Scholar
[5] Edwards, R. D. and Kirby, R., Deformation of spaces of imbeddings. Ann.Math. 93(1971), 63–88.Google Scholar
[6] Eilenberg, S., and Wilder, R. L., Uniform local connectedness and contractibility. Amer. J. Math. 64(1942), 613–622,Google Scholar
[7] Fathi, A., Structure of the group of homeomorphisms preserving a good measure on a compact manifold. Ann. Sci. École Norm. Sup. (4) 13(1980), no. 1, 45–93.Google Scholar
[8] Kuratowski, K., Sur le prolongement des fonctions continues et les transformations en polytopes. Fund. Math. 24(1935), 259–268.Google Scholar
[9] Kuratowski, K., Topology. Academic Press, New York (vol. I) 1966, (vol. II) 1968.Google Scholar
[10] Oxtoby, J., and Ulam, S., Measure preserving homeomorphisms and metrical transitivity. Ann. Math. 42(1941), 874–920.Google Scholar
[11] Whitehead, G. W., Elements of Homotopy Theory. Graduate Texts in Mathematics 61, Springer-Verlag, Berlin, 1978.Google Scholar