Burnside groups and n-moves for links

Haruko A. Miyazawa, Kodai Wada, Akira Yasuhara

Research output: Contribution to journalArticle

Abstract

M. K. Dabkowski and J. H. Przytycki introduced the nth Burnside group of a link, which is an invariant preserved by n-moves. Using this invariant, for an odd prime p, they proved that there are links which cannot be reduced to trivial links via p-moves. It is generally difficult to determine if pth Burnside groups associated to a link and the corresponding trivial link are isomorphic. In this paper, we give a necessary condition for the existence of such an isomorphism. Using this condition we give a simple proof for their results that concern p-move reducibility of links.

Original languageEnglish
Pages (from-to)3595-3602
Number of pages8
JournalProceedings of the American Mathematical Society
Volume147
Issue number8
DOIs
Publication statusPublished - 2019 Jan 1

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Trivial
Invariant
Reducibility
Isomorphism
Isomorphic
Odd
Necessary Conditions

Keywords

  • Burnside group
  • Fox coloring
  • Link
  • Magnus expansion
  • Montesinos-Nakanishi 3- move conjecture
  • Virtual link
  • Welded link

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Burnside groups and n-moves for links. / Miyazawa, Haruko A.; Wada, Kodai; Yasuhara, Akira.

In: Proceedings of the American Mathematical Society, Vol. 147, No. 8, 01.01.2019, p. 3595-3602.

Research output: Contribution to journalArticle

Miyazawa, Haruko A. ; Wada, Kodai ; Yasuhara, Akira. / Burnside groups and n-moves for links. In: Proceedings of the American Mathematical Society. 2019 ; Vol. 147, No. 8. pp. 3595-3602.
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