Concordances of Hilbert cube manifolds

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.