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2- AND 3-VARIATIONS AND FINITE TYPE INVARIANTS OF DEGREE 2 AND 3

MIGIWA SAKURAI

Division of Mathematics, Graduated School of Science, Tokyo Woman's Christian University, 2-6-1, Zempukuji, Suginami-ku, Tokyo 167-8585, Japan

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https://doi.org/10.1142/S0218216513500429Cited by:1 (Source: Crossref)

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.

Keywords:

AMSC: 57M25

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