Alternating links have representativity 2

Thomas Kindred

doi:10.2140/agt.2018.18.3339

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arXiv · 1703.03393

Alternating links have representativity 2

Thomas Kindred

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Abstract

We prove that if $L$ is a non-trivial alternating link embedded (without crossings) in a closed surface $F\subset S^3$, then $F$ has a compressing disk whose boundary intersects $L$ in no more than two points. Moreover, whenever the surface is incompressible and $\partial$-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. 2017-03-09. Alternating links have representativity 2. https://doi.org/10.2140/agt.2018.18.3339

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