Engulfing and Finitely Generated Groups
Engulfing and Finitely Generated Groups
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.