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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Concordances of Hilbert cube manifolds


Author: T. A. Chapman
Journal: Trans. Amer. Math. Soc. 219 (1976), 253-268
MSC: Primary 57A20; Secondary 57E05
DOI: https://doi.org/10.1090/S0002-9947-1976-0402754-8
MathSciNet review: 0402754
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Abstract: The main result of this paper asserts that homotopy groups of concordances of compact Hilbert cube manifolds are isomorphic to homotopy groups of concordances of compact finite-dimensional piecewise-linear manifolds. This enables us to apply some finite-dimensional results to obtain some new information about homotopy groups of homeomorphism groups of compact Hilbert cube manifolds. Our approach also yields a much shorter proof of the local contractibility of the homeomorphism group of any compact Hilbert cube manifold.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0402754-8
Keywords: Q-manifold, concordance, homeomorphism group, group of self-equivalences
Article copyright: © Copyright 1976 American Mathematical Society