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

Research output: Contribution to journalArticle

3 Citations (Scopus)

### 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 language English 1350042 Journal of Knot Theory and its Ramifications 22 8 https://doi.org/10.1142/S0218216513500429 Published - 2013 Jul 1 Yes

### Keywords

• finite type invariant
• local move
• Virtual knot

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

In: Journal of Knot Theory and its Ramifications, Vol. 22, No. 8, 1350042, 01.07.2013.

Research output: Contribution to journalArticle

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