English

A virtualized skein relation for a multivariable polynomial invariant

Geometric Topology 2022-03-29 v1

Abstract

The virtual skein relation for the Jones polynomial of the virtual link diagram was introduced by N. Kamada, S. Nakabo, and S. Satoh. H. A. Dye, L. H. Kauffman, and Y. Miyazawa introduced multivariable polynomial, an invariant of virtual links, which is a refinement of Jones polynomial. In this paper, we give a skein relation for the multivariable polynomials among positive, negative, and virtual crossings with some restrictions. We apply this relation to study some properties of virtual links obtained by replacing a real crossing by a virtual crossing.

Keywords

Cite

@article{arxiv.2203.14502,
  title  = {A virtualized skein relation for a multivariable polynomial invariant},
  author = {Moemi Hiraki},
  journal= {arXiv preprint arXiv:2203.14502},
  year   = {2022}
}

Comments

8 pages, 15 figures

R2 v1 2026-06-24T10:27:52.518Z