A polynomial invariant of virtual knots

Zhiyun Cheng

A polynomial invariant of virtual knots

Geometric Topology 2012-02-20 v1

Authors: Zhiyun Cheng

Abstract

The aim of this paper is to introduce a polynomial invariant $f_K(t)$ for virtual knots. We show that $f_K(t)$ can be used to distinguish some virtual knot from its inverse and mirror image. The behavior of $f_K(t)$ under connected sum is also given. Finally we discuss which kind of polynomial can be realized as $f_K(t)$ for some virtual knot $K$ .

Keywords

knot invariants jones polynomial knot theory

Cite

@article{arxiv.1202.3850,
  title  = {A polynomial invariant of virtual knots},
  author = {Zhiyun Cheng},
  journal= {arXiv preprint arXiv:1202.3850},
  year   = {2012}
}

Comments

11 pages, 16 figures

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