Virtual Thompson's group

Yuya Kodama; Akihiro Takano

doi:10.2969/jmsj/91339133

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arXiv · 2210.15990

Virtual Thompson's group

Yuya Kodama·Akihiro Takano

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Abstract

For virtual knot theory, the virtual braid group was defined by generalizing the braid group. It was proved that any virtual link can be obtained by the closure of a virtual braid. On the other hand, due to work by Jones et al., it is known that any (oriented) link is constructed from an element of Thompson's group $F$. In this paper, we define the ``virtual version'' of Thompson's group $F$ and prove that any virtual link is constructed from an element of the group.

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Yuya Kodama, Akihiro Takano. 2022-10-28. Virtual Thompson's group. https://doi.org/10.2969/jmsj%2F91339133

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