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The crossing number of satellite knots

Marc Lackenby
Algebraic & Geometric Topology 14 (2014) 2379–2409
DOI: 10.2140/agt.2014.14.2379
Abstract

We show that the crossing number of a satellite knot is at least 10−13 times the crossing number of its companion knot.

Keywords
satellite knot, crossing number
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 18 May 2012
Revised: 22 August 2013
Accepted: 1 November 2013
Published: 28 August 2014
Authors
Marc Lackenby
Mathematical Institute
University of Oxford
Radcliffe Observatory Quarter
Woodstock Road
Oxford OX2 6GG
UK