Special Issue on Virtual Knot Theory, Vol. IIINo Access

A LINKING NUMBER DEFINITION OF THE AFFINE INDEX POLYNOMIAL AND APPLICATIONS

Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, IL 60607, Chicago, USA

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and

LOUIS H. KAUFFMAN

Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, IL 60607, Chicago, USA

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https://doi.org/10.1142/S0218216513410046Cited by:27 (Source: Crossref)

Abstract

This paper gives an alternate definition of the Affine Index Polynomial (called the Wriggle Polynomial) using virtual linking numbers and explores applications of this polynomial. In particular, it proves the Cosmetic Crossing Change Conjecture for odd virtual knots and pure virtual knots. It also demonstrates that the polynomial can detect mutations by positive rotation and proves it cannot detect mutations by positive reflection. Finally it exhibits a pair of mutant knots that can be distinguished by a type 2 vassiliev invariant coming from the polynomial.

Keywords:

AMSC: 57M25, 54H05

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