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2018 Alternating links have representativity $2$
Thomas Kindred
Algebr. Geom. Topol. 18(6): 3339-3362 (2018). DOI: 10.2140/agt.2018.18.3339

Abstract

We prove that if L is a nontrivial alternating link embedded (without crossings) in a closed surface FS3, then F has a compressing disk whose boundary intersects L 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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Thomas Kindred. "Alternating links have representativity $2$." Algebr. Geom. Topol. 18 (6) 3339 - 3362, 2018. https://doi.org/10.2140/agt.2018.18.3339

Information

Received: 24 August 2017; Revised: 4 December 2017; Accepted: 11 April 2018; Published: 2018
First available in Project Euclid: 27 October 2018

zbMATH: 06990066
MathSciNet: MR3868223
Digital Object Identifier: 10.2140/agt.2018.18.3339

Subjects:
Primary: 57M25
Secondary: 57M50

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 6 • 2018
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