Illinois Journal of Mathematics

One-domination of knots

M. Boileau, S. Boyer, D. Rolfsen, and S. C. Wang

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds 55M25: Degree, winding number


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.

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