Codimension one embeddings of manifolds with locally flat triangulations

James Cecil Cantrell

Vol. 45 (1973), No. 1, 43–47

DOI: 10.2140/pjm.1973.45.43

Abstract

In this note investigations are made of the problem of deciding if a given codimension one submanifold 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, 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.

Mathematical Subject Classification

Primary: 57A45

Milestones

Received: 8 October 1971

Revised: 6 January 1972

Published: 1 March 1973