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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
DOI: https://doi.org/10.1090/S0002-9939-1986-0845998-5
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 $\mathcal {B} \subset \mathring {M}$, such that $K \subset \mathring {\mathcal {B}}$ if and only if ${\pi _1}(M\backslash K)$ is finitely generated.


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Keywords: <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$3$">-manifold, engulf, finitely generated
Article copyright: © Copyright 1986 American Mathematical Society