Dehn filling and the knot group I: Realization Property

Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito

Each $r$-Dehn filling of the exterior $E(K)$ of a knot $K$ in $S^3$ produces a $3$-manifold $K(r)$, and induces an epimorphism from the knot group $G(K)=\ddot{I}{€}_1(E(K))$ to $π_1(K(r)…