Link invariants derived from multiplexing of crossings

Haruko A. Miyazawa, Kodai Wada, Akira Yasuhara

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the multiplexing of a crossing, replacing a classical crossing of a virtual link diagram with multiple crossings which is a mixture of classical and virtual. For integers mi (i = 1, . . . , n) and an ordered n-component virtual link diagram D, a new virtual link diagram D(m1, . . . ,mn) is obtained from D by the multiplexing of all crossings. For welded isotopic virtual link diagrams D and D′, D(m1, . . . ,mn) and D′(m1, . . . ,mn) are welded isotopic. From the point of view of classical link theory, it seems very interesting that D(m1, . . . ,mn) could not be welded isotopic to a classical link diagram even if D is a classical one, and new classical link invariants are expected from known welded link invariants via the multiplexing of crossings.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2017 Aug 21
Externally publishedYes

Keywords

  • Alexander polynomial
  • Generalized link group
  • Multiplexing of crossings
  • Welded link

ASJC Scopus subject areas

  • General

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