Open Access
Spring 2016 One-domination of knots
M. Boileau, S. Boyer, D. Rolfsen, S. C. Wang
Illinois J. Math. 60(1): 117-139 (Spring 2016). DOI: 10.1215/ijm/1498032026


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.


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M. Boileau. S. Boyer. D. Rolfsen. S. C. Wang. "One-domination of knots." Illinois J. Math. 60 (1) 117 - 139, Spring 2016.


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

zbMATH: 1375.57010
MathSciNet: MR3665174
Digital Object Identifier: 10.1215/ijm/1498032026

Primary: 55M25 , 57M25 , 57M27

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

Vol.60 • No. 1 • Spring 2016
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