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Transactions of the American Mathematical Society

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



A weak characteristic pair for end-irreducible $ 3$-manifolds

Author: Bobby Neal Winters
Journal: Trans. Amer. Math. Soc. 341 (1994), 377-403
MSC: Primary 57N10; Secondary 57M10
MathSciNet review: 1182982
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Abstract: This extends a weakened version of the Characteristic Pair Theorem of Jaco, Shalen, and Johannson to a large subclass of the class of end-irreducible $ 3$-manifolds. The Main Theorem of this paper states that if $ (W,w)$ is a noncompact $ 3$-manifold pair (where $ W$ is a noncompact $ 3$-manifold that has an exhausting sequence with certain nice properties and where $ w$ is incompressible in $ W$), then there is a Seifert pair $ (\Sigma ,\Phi )$ contained in $ (W,w)$ such that any $ 2$-manifold that is strongly essential in $ (W,w)$ and each of whose components is a torus, an annulus, an open annulus, or a half-open annulus is isotopic in $ (W,w)$ into $ (\Sigma ,\Phi )$.

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Keywords: $ 3$-manifold, characteristic pair, end-irreducible, isotopy, noncompact
Article copyright: © Copyright 1994 American Mathematical Society

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