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An affine index polynomial invariant and the forbidden move of virtual knots

Migiwa Sakurai

National Institute of Technology, Ibaraki College, 866 Nakane, Hitachinaka-shi, Ibaraki-ken 312-8508, Japan

E-mail Address: migiwa@ge.ibaraki-ct.ac.jp

https://doi.org/10.1142/S0218216516500401Cited by:6 (Source: Crossref)

Abstract

Kauffman defines an affine index polynomial invariant for virtual knots. The invariant is induced from a numerical invariant called an $n$ $n$ -writhe. In this paper, we provide the difference of the values obtained from invariants between two virtual knots which can be transformed into each other by a single forbidden move. As a result, we make it possible for many virtual knots to determine the unknotting numbers by forbidden moves.

Keywords:

AMSC: 57M25

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