The Dabkowski-Sahi invariant and 4-moves for links

Haruko A. Miyazawa, Kodai Wada*, Akira Yasuhara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Dabkowski and Sahi defined an invariant of a link in the 3-sphere, which is preserved under 4-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish between the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to 4-moves.

Original languageEnglish
Article number46
JournalGeometriae Dedicata
Volume217
Issue number3
DOIs
Publication statusPublished - 2023 Jun
Externally publishedYes

Keywords

  • 4-move
  • Link
  • Link-homotopy
  • Magnus expansion
  • Welded link

ASJC Scopus subject areas

  • Geometry and Topology

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