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A PARITY AND A MULTI-VARIABLE POLYNOMIAL INVARIANT FOR VIRTUAL LINKS

YOUNG HO IM

Department of Mathematics, Pusan National University, Busan, 609-735, Korea

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and

KYOUNG IL PARK

Department of Mathematics, Pusan National University, Busan, 609-735, Korea

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https://doi.org/10.1142/S0218216513500739Cited by:3 (Source: Crossref)

Abstract

We introduce a parity of classical crossings of virtual link diagrams which extends the Gaussian parity of virtual knot diagrams and the odd writhe of virtual links that extends that of virtual knots introduced by Kauffman [A self-linking invariants of virtual knots, Fund. Math.184 (2004) 135–158]. Also, we introduce a multi-variable polynomial invariant for virtual links by using the parity of classical crossings, which refines the index polynomial introduced in [Index polynomial invariants of virtual links, J. Knot Theory Ramifications19(5) (2010) 709–725]. As consequences, we give some properties of our invariant, and raise some examples.

Keywords:

AMSC: 57M25, 57M27

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