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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.
Kodama et al. (Tue,) studied this question.
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