no. 5
The leading coefficient of the L 2 -Alexander torsion
[Le coefficient dominant de la torsion d’Alexander L 2 ]
Ben Aribi, Fathi ; Friedl, Stefan1 ; Herrmann, Gerrit1
1 Fakultät für Mathematik Universität Regensburg (Germany)
Annales de l'Institut Fourier, Tome 72 (2022) no. 5, pp. 1993-2035.

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.

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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3509
Classification : 57M25, 57M27
Keywords: $L^2$-invariants, $3$-manifolds, Thurston norm
Mot clés : invariants $L^2$, variétés de dimension 3, norme de Thurston
Ben Aribi, Fathi  ; Friedl, Stefan 1 ; Herrmann, Gerrit 1

1 Fakultät für Mathematik Universität Regensburg (Germany)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 72 (2022) no. 5, pp. 1993-2035. doi : 10.5802/aif.3509. https://aif.centre-mersenne.org/articles/10.5802/aif.3509/

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