On determinant of checkerboard colorable virtual knots

For classical knots, it is well known that their determinants mod \(8\) are classified by the Arf invariant. Boden and Karimi introduced a determinant of checkerboard colorable virtual knots. We prove that their determinant mod \(8\) is classified by the coefficient of \(z^2\) in the ascending polyn...

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Bibliographic Details
Published inarXiv.org
Main Authors Hatano, Tomoaki, Nozaki, Yuta
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.08.2024
Subjects
Knots
Mathematics - Geometric Topology
Polynomials
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Summary:For classical knots, it is well known that their determinants mod \(8\) are classified by the Arf invariant. Boden and Karimi introduced a determinant of checkerboard colorable virtual knots. We prove that their determinant mod \(8\) is classified by the coefficient of \(z^2\) in the ascending polynomial which is an extension of the Conway polynomial for classical knots.
ISSN:2331-8422
DOI:10.48550/arxiv.2408.01891