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Virtual links which are equivalent as twisted links


Authors: Naoko Kamada and Seiichi Kamada
Journal: Proc. Amer. Math. Soc. 148 (2020), 2273-2285
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/proc/14899
Published electronically: January 21, 2020
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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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Additional Information

Naoko Kamada
Affiliation: Graduate School of Natural Sciences, Nagoya City University, Mizuho-ku, Nagoya, Aichi 467-8501, Japan
Email: kamada@nsc.nagoya-cu.ac.jp

Seiichi Kamada
Affiliation: Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: kamada@math.sci.osaka-u.ac.jp

DOI: https://doi.org/10.1090/proc/14899
Keywords: Virtual links, twisted links
Received by editor(s): August 24, 2018
Received by editor(s) in revised form: September 23, 2019
Published electronically: January 21, 2020
Additional Notes: The authors were supported by JSPS KAKENHI Grant Numbers JP15K04879, JP26287013, JP19K03496, and JP19H01788.
Communicated by: David Futer
Article copyright: © Copyright 2020 American Mathematical Society