English

The intersection polynomials of a virtual knot I: Definitions and calculations

Geometric Topology 2022-01-26 v2

Abstract

We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. The calculations of intersection polynomials are given up to crossing number four. We also study several properties of intersection polynomials.

Keywords

Cite

@article{arxiv.2102.12067,
  title  = {The intersection polynomials of a virtual knot I: Definitions and calculations},
  author = {Ryuji Higa and Takuji Nakamura and Yasutaka Nakanishi and Shin Satoh},
  journal= {arXiv preprint arXiv:2102.12067},
  year   = {2022}
}

Comments

27 pages, 22 figures. We divide the original version into four papers