Analytic, Reidemeister and homological torsion for congruence three–manifolds
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 3, pp. 417-469.

For a given Bianchi group Γ and certain natural coefficent modules V and sequences Γ n of congruence subgroups of Γ we give a conjecturally optimal upper bound for the size of the torsion subgroup of H 1 (Γ n ;V ). We also prove limit multiplicity results for the irreducible components of L cusp 2 (Γ n SL 2 ()).

Soit Γ un groupe de Bianchi. Pour certains Γ-modules V , et suites Γ n de sous-groupes de congruence de Γ nous démontrons une borne supérieure, conjecturée optimale, pour la taille du sous-groupe de torsion de l’homologie H 1 (Γ n ,V ). On démontre aussi des résultats de multiplicités limites pour les facteurs irréductibles des espaces L cusp 2 (Γ n SL 2 ()).

Published online:
DOI: 10.5802/afst.1605
Classification: 11F75, 11F72, 22E40, 57M10
Keywords: Congruence groups, hyperbolic manifolds, homology

Jean Raimbault 1

1 Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jean Raimbault. Analytic, Reidemeister and homological torsion for congruence three–manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 3, pp. 417-469. doi : 10.5802/afst.1605. https://afst.centre-mersenne.org/articles/10.5802/afst.1605/

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