Special Issue on Virtual Knot Theory, Vol. IIINo Access

A POLYNOMIAL INVARIANT OF VIRTUAL LINKS

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China

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and

HONGZHU GAO

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China

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https://doi.org/10.1142/S0218216513410022Cited by:48 (Source: Crossref)

Abstract

In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms [Parity in knot theory, Sb. Math.201 (2010) 693–733] to obtain a new polynomial invariant of virtual knots. This invariant can be regarded as a generalization of the odd writhe polynomial defined by the first author in [A polynomial invariant of virtual knots, preprint (2012), arXiv:math.GT/1202.3850v1]. The relation between this new polynomial invariant and the affine index polynomial [An affine index polynomial invariant of virtual knots, J. Knot Theory Ramification22 (2013) 1340007; A linking number definition of the affine index polynomial and applications, preprint (2012), arXiv:1211.1747v1] is discussed. In the second part we introduce a polynomial invariant for long flat virtual knots. In the third part we define a polynomial invariant for 2-component virtual links. This polynomial invariant can be regarded as a generalization of the linking number.

Keywords:

AMSC: 57M25, 57M27

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