2- and 3-variations and finite type invariants of degree 2 and 3

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Abstract

Goussarov, Polyak and Viro defined a finite type invariant and a local move called an n-variation for virtual knots. In this paper, we give the differences of the values of the finite type invariants of degree 2 and 3 between two virtual knots which can be transformed into each other by a 2- and 3-variation, respectively. As a result, we obtain lower bounds of the distance between long virtual knots by 2-variations and the distance between virtual knots by 3-variations by using the values of the finite type invariants of degree 2 and 3, respectively.

Original languageEnglish
Article number1350042
JournalJournal of Knot Theory and its Ramifications
Volume22
Issue number8
DOIs
Publication statusPublished - 2013 Jul 1

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Keywords

  • Virtual knot
  • finite type invariant
  • local move

ASJC Scopus subject areas

  • Algebra and Number Theory

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