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(K) n2w(J), where w( ) 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