#### Volume 18, issue 1 (2018)

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Width of a satellite knot and its companion

### Qilong Guo and Zhenkun Li

Algebraic & Geometric Topology 18 (2018) 1–13
##### Abstract

In this paper, we give a proof of a conjecture which says that $w\left(K\right)\ge {n}^{2}w\left(J\right)$, where $w\left(\phantom{\rule{0.3em}{0ex}}\cdot \phantom{\rule{0.3em}{0ex}}\right)$ is the width of a knot, $K$ is a satellite knot with $J$ as its companion, and $n$ is the winding number of the pattern. We also show that equality holds if $K$ is a satellite knot with braid pattern.

##### Keywords
width, satellite knots, companion, pattern, winding number
##### Mathematical Subject Classification 2010
Primary: 57M25, 57M27
##### Publication
Received: 25 November 2014
Revised: 15 May 2017
Accepted: 14 July 2017
Published: 10 January 2018
##### Authors
 Qilong Guo College of Science China University of Petroleum-Beijing Beijing China Zhenkun Li Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States