Virtual links which are equivalent as twisted links

Kamada, Naoko; Kamada, Seiichi

doi:10.1090/proc/14899

Virtual links which are equivalent as twisted links
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by Naoko Kamada and Seiichi Kamada PDF

Proc. Amer. Math. Soc. 148 (2020), 2273-2285 Request permission

Abstract:

A virtual link is a generalization of a classical link that is defined as an equivalence class of certain diagrams, called virtual link diagrams. It is further generalized to a twisted link. Twisted links are in one-to-one correspondence with stable equivalence classes of links in oriented thickenings of (possibly nonorientable) closed surfaces. By definition, equivalent virtual links are also equivalent as twisted links. In this paper, we discuss when two virtual links are equivalent as twisted links, and give a necessary and sufficient condition for this to be the case.

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