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

Ryuji Higa; Takuji Nakamura; Yasutaka Nakanishi; Shin Satoh

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arXiv · 2102.12067

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

Ryuji Higa·Takuji Nakamura·Yasutaka Nakanishi·Shin Satoh

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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.

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Ryuji Higa, Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh. 2021-02-24. The intersection polynomials of a virtual knot I: Definitions and calculations. https://arxiv.org/abs/2102.12067

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