Knot Group Epimorphisms, II

Details Knot Group Epimorphisms, II Knot Group Epimorphisms, II

2008-06-19

arxiv.org/abs/0806.3223v1

Mathematics

Geometric Topology

14 pages, 1 figure

Scientific paper

We consider the relations $\ge$ and $\ge_p$ on the collection of all knots, where $k \ge k'$ (respectively, $k \ge_p k'$) if there exists an epimorphism $\pi k \to \pi k'$ of knot groups (respectively, preserving peripheral systems). When $k$ is a torus knot, the relations coincide and $k'$ must also be a torus knot; we determine the knots $k'$ that can occur. If $k$ is a 2-bridge knot and $k \ge_p k'$, then $k'$ is a 2-bridge knot with determinant a proper divisor of the determinant of $k$; only finitely many knots $k'$ are possible.

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