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.
Citation
M. Boileau. S. Boyer. D. Rolfsen. S. C. Wang. "One-domination of knots." Illinois J. Math. 60 (1) 117 - 139, Spring 2016. https://doi.org/10.1215/ijm/1498032026
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