English

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 L2L^2-Alexander torsions of a 33-manifold MM in terms of hyperbolic volumes and of relative L2L^2-torsions of sutured manifolds obtained by cutting MM 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