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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Constructing isotopes on noncompact $3$-manifolds

Author: Marianne S. Brown
Journal: Trans. Amer. Math. Soc. 180 (1973), 237-263
MSC: Primary 57A10
MathSciNet review: 0331393
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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 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.

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Article copyright: © Copyright 1973 American Mathematical Society