Year: 2008
Type: preprint
Abstract: 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 $πk \to πk'$ 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.
Source: arXiv (Cornell University)
Authors: Silver, Daniel S., Whitten, Wilbur
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2139424034