Structures on M × R

Abstract

A central role in the theory of smoothing combinatorial manifolds is played by the Cairns–Hirsch Theorem, which may be expressed (in a weak form) as follows:If M is a combinatorial manifold and if M × R has a differentiable structure a, compatible with its combinatorial structure then M has a differentiable structure λ, such that (M × R)α is diffeomorphic with Mλ × R.