On the Homeomorphism group problem of Compact manifolds
by
Raymond Y Wong
Univ of California, Santa Barbara

Let M be a compact n-manifold. It has been a long standing problem to decide whether the space of homeomorphism H(M) is an ANR. It is known that H(M) is locally contractible and for n = 1, 2 or infinite (the Hilbert cube-manifold), H(M) is indeed an ANR. Moreover, various subgroups of H(M) (PL and Lipschitz) and are shown to be manifolds if H(M) is an ANR. H(M) is naturally imbedded in H(M x Q), the space of homeomorphisms of the Q-manifold M x Q, where Q = Hilbert cube. In this talk I will outline a procedure for constructing a retraction of a countable dense subset of H(M x Q) into H(M) and discuss whether such a procedure would yield a retraction of H(M x Q) onto H(M).

Date received: May 19, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-17.