Link invariants derived from multiplexing of crossings

Haruko Aida Miyazawa, Kodai Wada, Akira Yasuhara

Research output: Contribution to journalArticle

Abstract

We introduce the multiplexing of a crossing, replacing a classical crossing of a virtual link diagram with a mixture of classical and virtual crossings. 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, the virtual link diagrams D(m1,…, mn) and D(m1,…, mn) are welded isotopic. From the point of view of classical link theory, it seems very interesting that new classical link invariants are obtained from welded link invariants via the multiplexing of crossings.

Original languageEnglish
Pages (from-to)2497-2507
Number of pages11
JournalAlgebraic and Geometric Topology
Volume18
Issue number4
DOIs
Publication statusPublished - 2018 Apr 26

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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