Embeddings of bounded manifolds

Abstract

Introduction. This paper gives some embedding and unknotting theorems for bounded manifolds in the PL and differential categories. The theorems are of a similar nature to the embedding and unknotting theorems of Irwin and Zeeman (9, 18), except that the boundaries are allowed to move and the appropriate connectivity conditions become conditions on the relative homotopy groups of the manifolds modulo the boundary, or some suitable part of the boundary.