Constructing isotopes on noncompact $3$manifolds
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 by Marianne S. Brown PDF
 Trans. Amer. Math. Soc. 180 (1973), 237263 Request permission
Abstract:
We consider the question “When are two homeomorphisms of a noncompact $3$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 $3$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 endirreducible; 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.References

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Additional Information
 © Copyright 1973 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 180 (1973), 237263
 MSC: Primary 57A10
 DOI: https://doi.org/10.1090/S0002994719730331393X
 MathSciNet review: 0331393