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

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 ()).

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 ()).

Publié le :
DOI : https://doi.org/10.5802/afst.1605
Classification : 11F75,  11F72,  22E40,  57M10
Mots clés : Congruence groups, hyperbolic manifolds, homology
@article{AFST_2019_6_28_3_417_0,
     author = {Jean Raimbault},
     title = {Analytic, {Reidemeister} and homological torsion for congruence three{\textendash}manifolds},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {417--469},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {3},
     year = {2019},
     doi = {10.5802/afst.1605},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1605/}
}
Jean Raimbault. Analytic, Reidemeister and homological torsion for congruence three–manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 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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