A collaring theorem for codimension one manifolds

Abstract

The chief result implies that an n n -manifold S S embedded in the interior of an ( n + 1 ) (n + 1) -manifold M M as a closed, separating subset is locally flatly embedded if the embedding is well behaved in a locally peripheral sense and if S S has arbitrarily close neighborhoods Q Q such that the fundamental groups of appropriate components of Q ∖ S Q\backslash S admit a uniform finite upper bound on the number of generators.