Manifolds with non-stable fundamental groups at infinity

Abstract

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open $n$–manifold ($n\ge 7$). This paper may be viewed as a generalization of Siebenmann’s famous collaring theorem to open manifolds with non-stable fundamental group systems at infinity.