Engulfing and finitely generated groups

Skora, Richard

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

Engulfing and finitely generated groups
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Proc. Amer. Math. Soc. 97 (1986), 734-736 Request permission

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.

References

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Richard Skora, Cantor sets in $S^3$ with simply connected complements, Topology Appl. 24 (1986), no. 1-3, 181–188. Special volume in honor of R. H. Bing (1914–1986). MR 872489, DOI 10.1016/0166-8641(86)90060-X

A certain open manifold whose group is unity

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