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arXiv · 2504.01714

On Thompson knot theory and conjugacy classes of Thompson's group $F$

Yuanyuan Bao·Xiaobing Sheng
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Abstract

Jones introduced a method to produce unoriented links from elements of the Thompson's group $F$, and proved that any link can be produced by this construction. In this paper, we attempt to investigate the relations between conjugacy classes of the group $F$ and the links being constructed. For each unoriented link $L$, we find a sequence of elements of $F$ from distinct conjugacy classes which yield $L$ via Jones's construction. We also show that a sequence of $2$-bridge links can be constructed from elements in the conjugacy class of $x_0$ (resp. $x_1$).

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Yuanyuan Bao, Xiaobing Sheng. 2025-04-02. On Thompson knot theory and conjugacy classes of Thompson's group $F$. https://arxiv.org/abs/2504.01714

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