Alexander's theorem for stabilizer subgroups of Thompson's group

Yuya Kodama; Akihiro Takano

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arXiv · 2306.13398

Alexander's theorem for stabilizer subgroups of Thompson's group

Yuya Kodama·Akihiro Takano

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Abstract

In 2017, Jones studied the unitary representations of Thompson's group $F$ and defined a method to construct knots and links from $F$. One of his results is that any knot or link can be obtained from an element of this group, which is called Alexander's theorem. On the other hand, Thompson's group $F$ has many subgroups and it is known that there exist various subgroups which satisfy or do not satisfy Alexander's theorem. In this paper, we prove that almost all stabilizer subgroups under the natural action on the unit interval satisfy Alexander's theorem.

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Yuya Kodama, Akihiro Takano. 2023-06-23. Alexander's theorem for stabilizer subgroups of Thompson's group. https://arxiv.org/abs/2306.13398

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