Geodesic
Alternating links have representativity 2
Kindred, Thomas1
1 Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3339-3362

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove that if L is a nontrivial alternating link embedded (without crossings) in a closed surface F ⊂ S3, 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.

DOI : 10.2140/agt.2018.18.3339
Classification : 57M25, 57M50
Keywords: alternating knot, alternating link, representativity, closed surface, compressing disk

Kindred, Thomas 1

1 Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, United States 
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Kindred, Thomas. Alternating links have representativity 2. Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3339-3362. doi: 10.2140/agt.2018.18.3339

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