Linking invariants of even virtual links

Haruko A. Miyazawa, Kodai Wada*, Akira Yasuhara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


A virtual link diagram is even if the virtual crossings divide each component into an even number of arcs. The set of even virtual link diagrams is closed under classical and virtual Reidemeister moves, and it contains the set of classical link diagrams. For an even virtual link diagram, we define a certain linking invariant which is similar to the linking number. In contrast to the usual linking number, our linking invariant is not preserved under the forbidden moves. In particular, for two fused isotopic even virtual link diagrams, the difference between the linking invariants of them gives a lower bound of the minimal number of forbidden moves needed to deform one into the other. Moreover, we give an example which shows that the lower bound is best possible.

Original languageEnglish
Article number1750072
JournalJournal of Knot Theory and its Ramifications
Issue number12
Publication statusPublished - 2017 Oct 1
Externally publishedYes


  • Linking invariant
  • even virtual link
  • fused isotopy
  • virtual link

ASJC Scopus subject areas

  • Algebra and Number Theory


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