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Alternating links have
representativity $2$
Thomas Kindred |
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Algebraic & Geometric Topology 18 (2018) 3339–3362
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Abstract |
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We prove that if is a nontrivial alternating link embedded (without crossings) in a closed surface , then has a compressing disk whose boundary intersects in no more than two points. Moreover, whenever the surface is incompressible and –incompressible in the link exterior, it can be isotoped to have a standard tube at some crossing of any reduced alternating diagram. |
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Keywords
alternating knot, alternating link, representativity,
closed surface, compressing disk
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M50
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References |
Publication
Received: 24 August 2017
Revised: 4 December 2017
Accepted: 11 April 2018
Published: 18 October 2018
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Authors |
| Thomas Kindred | |
| Department of Mathematics University of Nebraska-Lincoln Lincoln, NE United States |
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| http://www.thomaskindred.com | |
