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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on stable homeomorphisms of infinite-dimensional manifolds
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by Raymond Y. T. Wong PDF
Proc. Amer. Math. Soc. 28 (1971), 271-272 Request permission

Abstract:

In papers by R. D. Anderson and R. Wong, respectively, it is shown that all homeomorphisms of the Hilbert cube onto itself, or of the infinite dimensional separable Hilbert space ${l_2}$ onto itself, are stable in the sense of Brown-Gluck. These facts can be used to show that all homeomorphisms of $X$ onto itself are isotopic to the identity mapping where $X$ is either the Hilbert cube or ${l_2}$. It follows that some versions of the infinite-dimensional annulus conjecture are true. In this note we give a simple proof of Anderson’s result. It follows from Brown-Gluck’s technique that for any connected manifold $X$ modeled on $Q$ or $s$, every homeomorphism of $X$ onto itself is stable.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 271-272
  • MSC: Primary 57.55
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0271996-8
  • MathSciNet review: 0271996