1-domination of knots

Abstract

We say that a knot $k_1$ in the $3$-sphere {\it $1$-dominates} another $k_2$ if there is a proper degree 1 map $E(k_1)\to E(k_2)$ between their exteriors, and write $k_1\ge k_2$. When $k_1\ge k_2$ but $k_1\ne k_2$ we write $k_1>k_2$. One expects in the latter eventuality that $k_1$ is more {\it complicated}. In this paper we produce various sorts of evidence to support this philosophy.

References in corpus (3)

• Epimorphisms between 2-bridge link groups
• Non-zero degree maps between $2n$-manifolds
• Finiteness of nonzero degree maps between three-manifolds

Cited by in corpus (2)

• Brouwer degree, domination of manifolds, and groups presentable by products
• Computing twisted Alexander polynomials for Montesinos links