Annular Links from Thompson's Group $T$

Louisa Liles

doi:10.2140/agt.2025.25.5013

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arXiv · 2401.12065

Annular Links from Thompson's Group $T$

Louisa Liles

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Abstract

In 2014 Jones showed how to associate links in the $3$-sphere to elements of Thompson's group $F$. We provide an analogue of this program for annular links and Thompson's group $T$. The main result is that any edge-signed graph embedded in the annulus is the Tait graph of an annular link built from an element of $T$. In analogy to the work of Aiello and Conti, we also show that the coefficients of certain unitary representations of $T$ recover the Jones polynomial of annular links.

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Louisa Liles. 2024-01-22. Annular Links from Thompson's Group $T$. https://doi.org/10.2140/agt.2025.25.5013

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