The leading coefficient of the L 2 -Alexander torsion
Annales de l'Institut Fourier, Online first, 43 p.

We give upper and lower bounds on the leading coefficients of the L 2 -Alexander torsions of a 3-manifold M in terms of hyperbolic volumes and of relative L 2 -torsions of sutured manifolds obtained by cutting M 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.

Nous trouvons des bornes supérieure et inférieure des coefficients dominants des torsions d’Alexander L 2 d’une variété de dimension 3 M, en fonction de volumes hyperboliques et de torsions L 2 relatives de variétés suturées qu’on obtient en découpant M le long de certaines surfaces.

Nous démontrons que pour de nombreuses familles d’extérieurs de nœuds, les bornes inférieure et supérieure sont égales, notamment pour les extérieurs des nœuds à deux ponts. En particulier, nous calculons explicitement le coefficient dominant pour les nœuds à deux ponts.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3509
Classification: 57M25,  57M27
Keywords: L 2 -invariants, 3-manifolds, Thurston norm
Ben Aribi, Fathi ; Friedl, Stefan 1; Herrmann, Gerrit 1

1 Fakultät für Mathematik Universität Regensburg (Germany)
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Ben Aribi, Fathi; Friedl, Stefan; Herrmann, Gerrit. The leading coefficient of the $L^2$-Alexander torsion. Annales de l'Institut Fourier, Online first, 43 p.

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