Compact Hilbert cube manifolds and the invariance of Whitehead torsion

Abstract

In this note we prove that every compact metric manifold modeled on the Hilbert cube Q is homeomorphic to \K\ x Q, for some finite simplicial complex K. We also announce an affirmative answer to the question concerning the topological invariance of Whitehead torsion for compact, connected CW-complexes. As a corollary of this latter result it follows that two compact Hilbert cube manifolds are homeomorphic iff their associated polyhedra (in the sense above) have the same simple homotopy type.