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

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
Received: 8 October 1971
Revised: 6 January 1972
Published: 1 March 1973
James Cecil Cantrell