Topological manifolds of dimension ≠4 have a Lipschitz structure. [Ed: Is this "well-known"? Is it obvious? Can somebody give a reference?] Does this imply the following result?

Assume M and N are smooth Riemannian manifold, with same dimension other than 4. If M homeomorphic to N, then M is bi-Lipschitz homeomorphic to N.

In other words, can two manifolds (of dimension ≠4) be homeomorphic without being bi-Lipschitz homeomorphic?

thatbad, Theo, surely? My reading of it is as a question about whether two (Riemannian) smooth manifolds of dimension $\ne 4$ can be homeomorphic without being bi-Lipshitz holomorphic. – Yemon Choi Mar 30 '10 at 23:08