## Illinois Journal of Mathematics

### One-domination of knots

#### Abstract

We say that a knot $k_{1}$ in the $3$-sphere $1$-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 complicated. In this paper, we produce various sorts of evidence to support this philosophy.

#### Article information

Source
Illinois J. Math., Volume 60, Number 1 (2016), 117-139.

Dates
Received: 2 September 2015
Revised: 15 April 2016
First available in Project Euclid: 21 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1498032026

Digital Object Identifier
doi:10.1215/ijm/1498032026

Mathematical Reviews number (MathSciNet)
MR3665174

Zentralblatt MATH identifier
1375.57010

#### Citation

Boileau, M.; Boyer, S.; Rolfsen, D.; Wang, S. C. One-domination of knots. Illinois J. Math. 60 (2016), no. 1, 117--139. doi:10.1215/ijm/1498032026. https://projecteuclid.org/euclid.ijm/1498032026