Codimension one embeddings of manifolds with locally flat triangulations
James C. Cantrell · Pacific Journal of Mathematics · 1973
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.