A diagrammatic computation of abelian link invariants
Geometric Topology
2025-11-26 v2
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].
Cite
@article{arxiv.2405.17011,
title = {A diagrammatic computation of abelian link invariants},
author = {David Cimasoni and Livio Ferretti and Jessica Liu},
journal= {arXiv preprint arXiv:2405.17011},
year = {2025}
}
Comments
19 pages, 11 figures; minor changes in v2 following suggestions by referee; accepted version, to appear in AGT