Constructing isotopes on noncompact 3-manifolds

Abstract

We consider the question “When are two homeomorphisms of a noncompact 3 3 -manifold onto itself isotopic?” Roughly, the answer is when they are homotopic to each othet. More precisely, this paper deals with the question for irreducible 3 3 -manifolds which either have an infinite hierarchy or have such a hierarchy after the removal of a compact set. Manifolds having the first property are called end-irreducible; the others are called eventually endirreducible. There are two results fot each type of manifold depending on whether the homotopy between the two homeomorphisms sends the boundary of the manifold into itself or not.