Vol. 45, No. 1, 1973

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Codimension one embeddings of manifolds with locally flat triangulations

James Cecil Cantrell

Vol. 45 (1973), No. 1, 43–47
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
Authors
James Cecil Cantrell