The intersection polynomials of a virtual knot IV: Crossing change and supporting genus

In the previous papers, we introduced three intersection polynomials of a virtual knot. In this paper, we prove that the first and second intersection polynomials are finite-type invariants of order two with respect to crossing change. We also study virtual knots of supporting genus one, and give a relation between the first and second intersection polynomials of such a virtual knot.

Authors

Takuji Nakamura (ORCID: https://orcid.org/0000-0002-3876-2946)
Ryuji Higa
Shin Satoh (ORCID: https://orcid.org/0000-0002-4918-3683)
Yasutaka Nakanishi (ORCID: https://orcid.org/0000-0001-8724-0338)

Institutions

Takeda (Japan) (JP)
Kobe University (JP)
University of Yamanashi (JP)

Publication Details

Journal: Journal of Knot Theory and Its Ramifications
Published: 2025-01-10
DOI: https://doi.org/10.1142/s0218216525500087
Citations: 1
Primary Topic: Botulinum Toxin and Related Neurological Disorders
Type: article
Field-Weighted Citation Impact: 1.39

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article

The intersection polynomials of a virtual knot IV: Crossing change and supporting genus

Takuji Nakamura, Ryuji Higa, Shin Satoh, Yasutaka Nakanishi

Jan 10, 2025

1 citations

Journal of Knot Theory and Its Ramifications

Botulinum Toxin and Related Neurological Disorders

1.39

article

The intersection polynomials of a virtual knot IV: Crossing change and supporting genus

Takuji Nakamura, Ryuji Higa, Shin Satoh, Yasutaka Nakanishi

January 10, 2025article en

1 citations

Abstract

In the previous papers, we introduced three intersection polynomials of a virtual knot. In this paper, we prove that the first and second intersection polynomials are finite-type invariants of order two with respect to crossing change. We also study virtual knots of supporting genus one, and give a relation between the first and second intersection polynomials of such a virtual knot.

Journal of Knot Theory and Its RamificationsVol. 34(04)

Takeda (Japan) (JP), Kobe University (JP), University of Yamanashi (JP)

Openalex Percentile: Top 25%

Botulinum Toxin and Related Neurological Disorders

1.39

DOI Source OpenAlex

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The intersection polynomials of a virtual knot IV: Crossing change and supporting genus — Takuji Nakamura, Ryuji Higa, et al. · Journal of Knot Theory and Its Ramifications (2025) | TGRS Research Map | TGRS