Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A note on stable homeomorphisms of infinite-dimensional manifolds


Author: Raymond Y. T. Wong
Journal: Proc. Amer. Math. Soc. 28 (1971), 271-272
MSC: Primary 57.55
MathSciNet review: 0271996
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57.55

Retrieve articles in all journals with MSC: 57.55


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0271996-8
PII: S 0002-9939(1971)0271996-8
Keywords: Homeomorphisms, stable homeomorphisms, Hilbert cube
Article copyright: © Copyright 1971 American Mathematical Society