The leading coefficient of the $L^2$-Alexander torsion
Geometric Topology
2021-05-07 v2
Abstract
We give upper and lower bounds on the leading coefficients of the -Alexander torsions of a -manifold in terms of hyperbolic volumes and of relative -torsions of sutured manifolds obtained by cutting along certain surfaces. We prove that for numerous families of knot exteriors the lower and upper bounds are equal, notably for exteriors of 2-bridge knots. In particular we compute the leading coefficient explicitly for 2-bridge knots.
Keywords
Cite
@article{arxiv.1806.10965,
title = {The leading coefficient of the $L^2$-Alexander torsion},
author = {Fathi Ben Aribi and Stefan Friedl and Gerrit Herrmann},
journal= {arXiv preprint arXiv:1806.10965},
year = {2021}
}
Comments
v2, final version : 33 pages, 5 figures. we rewrote parts of the paper, we added details to the proofs and we added Figure 3 for clarity, but the mathematical content is globally unchanged. Accepted for publication at the Annales de l'Institut Fourier