Determining isotopy classes of crossing arcs in alternating links

Anastasiia Tsvietkova

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arXiv · 1411.0231

Determining isotopy classes of crossing arcs in alternating links

Anastasiia Tsvietkova

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Abstract

Given a reduced alternating diagram for a link, we obtain conditions that guarantee that the link complement has a complete hyperbolic structure, crossing arcs are the edges of an ideal geodesic triangulation, and every crossing arc is isotopic to a simple geodesic. The latter was conjectured by Sakuma and Weeks in 1995. We provide infinite families of closed braids for which our conditions hold.

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BibTeX RIS

Anastasiia Tsvietkova. 2014-11-02. Determining isotopy classes of crossing arcs in alternating links. https://arxiv.org/abs/1411.0231

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