The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds

Stavros Garoufalidis; Seokbeom Yoon

doi:10.1112/blms.70145

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arXiv · 2401.01536

The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds

Stavros Garoufalidis·Seokbeom Yoon

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Abstract

We establish a connection between the Alexander polynomial of a knot and its twisted and $L^2$-versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier matrices of ordered ideal triangulations and use them to provide formulas for the Alexander polynomial and its variants, the twisted Alexander polynomial and the $L^2$-Alexander torsion.

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Stavros Garoufalidis, Seokbeom Yoon. 2024-01-03. The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds. https://doi.org/10.1112/blms.70145

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