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A diagrammatic computation of abelian link invariants (2405.17011v2)
Published 27 May 2024 in math.GT
Abstract: 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].
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