A diagrammatic computation of abelian link invariants

Fuente: arXiv
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Auteurs principaux: Cimasoni, David, Ferretti, Livio, Liu, Jessica
Format: Preprint
Publié: 2024
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author Cimasoni, David
Ferretti, Livio
Liu, Jessica
author_facet Cimasoni, David
Ferretti, Livio
Liu, Jessica
contents We show how the multivariable signature and Alexander polynomial of a colored link can be computed from a single symmetric matrix naturally defined from a colored link diagram. In the case of a single variable, it coincides with the matrix introduced by Kashaev in [arXiv:1801.04632], which was recently proven to compute the Levine-Tristram signature and the Alexander polynomial of oriented links [arXiv:2311.01923, arXiv:2310.16729]. As a corollary, we obtain a multivariable extension of Kauffman's determinantal model of the Alexander polynomial, recovering a result of Zibrowius [arXiv:1601.04915v1].
format Preprint
id arxiv_https___arxiv_org_abs_2405_17011
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A diagrammatic computation of abelian link invariants
Cimasoni, David
Ferretti, Livio
Liu, Jessica
Geometric Topology
57K10
We show how the multivariable signature and Alexander polynomial of a colored link can be computed from a single symmetric matrix naturally defined from a colored link diagram. In the case of a single variable, it coincides with the matrix introduced by Kashaev in [arXiv:1801.04632], which was recently proven to compute the Levine-Tristram signature and the Alexander polynomial of oriented links [arXiv:2311.01923, arXiv:2310.16729]. As a corollary, we obtain a multivariable extension of Kauffman's determinantal model of the Alexander polynomial, recovering a result of Zibrowius [arXiv:1601.04915v1].
title A diagrammatic computation of abelian link invariants
topic Geometric Topology
57K10
url https://arxiv.org/abs/2405.17011