Engulfing and finitely generated groups

Skora, Richard

doi:10.1090/S0002-9939-1986-0845998-5

Engulfing and finitely generated groups
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by Richard Skora

Proc. Amer. Math. Soc. 97 (1986), 734-736

DOI: https://doi.org/10.1090/S0002-9939-1986-0845998-5

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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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A certain open manifold whose group is unity

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