Virtual Thompson's group
Yuya Kodama, Akihiro Takano · Journal of the Mathematical Society of Japan · 2024
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.