Width of a satellite knot and its companion

Guo, Qilong; Li, Zhenkun

doi:10.2140/agt.2018.18.1

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Width of a satellite knot and its companion

Qilong Guo and Zhenkun Li

Algebraic & Geometric Topology 18 (2018) 1–13

DOI: 10.2140/agt.2018.18.1

Abstract

In this paper, we give a proof of a conjecture which says that $w (K) \geq n^{2} w (J)$ , where $w (\cdot)$ 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

References

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

Volume 18, issue 1 (2018)