Smoothing a topological manifold

When can a topological manifold be smoothed—i.e., when does its (maximal) topological atlas contain a smooth subatlas? In 1940, S.S. Cairns gave sufficient conditions for such a smoothing [Ann. of Math. 41 (1940) 796–808], and in 1961 J.H.C. Whitehead perfected Cairnsʹ ideas; see [Ann. of Math. 73 (1961) 154–211, especially p. 164]. Using dynamical systems methods, I give a new proof of an improved Cairns–Whitehead Theorem. The improvement consists of a Lipschitz bound expressing a numerical criterion for smoothability.