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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Engulfing and finitely generated groups


Author: Richard Skora
Journal: Proc. Amer. Math. Soc. 97 (1986), 734-736
MSC: Primary 57N10; Secondary 57M05, 57N30
MathSciNet review: 845998
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Abstract: Let $ M$ be a simply connected $ 3$-manifold and $ K$ a piecewiselinear, simple loop in the interior of $ M$. It is shown that there is a piecewiselinear, homotopy $ 3$-ball $ \mathcal{B} \subset {\text{ }}\mathop M\limits^ \circ $, such that $ K \subset {\text{ }}\mathop \mathcal{B}\limits^ \circ $ if and only if $ {\pi _1}(M\backslash K)$ is finitely generated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0845998-5
PII: S 0002-9939(1986)0845998-5
Keywords: $ 3$-manifold, engulf, finitely generated
Article copyright: © Copyright 1986 American Mathematical Society