Codimension one embeddings of manifolds with locally flat triangulations

Abstract

In this note investigations are made of the problem of deciding if a given codimension one submanif old M is locally flat in the ambient manifold N. The principal result is that if M has a locally flat triangulation in which each closed simplex is locally flat in N 9 then M is locally flat in N. This allows one to establish for simplicial homotopy manifolds certain local flatness criteria that had been previously known for PL manifolds.