The (twisted/L²)-Alexander polynomial of ideally triangulated 3-manifolds

2024/01/03 by Garoufalidis, Stavros, Yoon, Seokbeom
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2401.01536

Abstract

We establish a connection between the Alexander polynomial of a knot and its twisted and L²-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 L²-Alexander torsion.

Related

• A survey of twisted Alexander polynomials
• Three flavors of twisted invariants of knots
• The L²-Alexander torsion of 3-manifolds
• Twisted Alexander invariant and non-abelian Reidemeister torsion for hyperbolic three-dimensional manifolds with cusps
• Twisted Alexander Polynomials of Hypersurface Complements