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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.

Compact Hilbert cube manifolds and the invariance of Whitehead torsion