For a given Bianchi group and certain natural coefficent modules and sequences of congruence subgroups of we give a conjecturally optimal upper bound for the size of the torsion subgroup of . We also prove limit multiplicity results for the irreducible components of .
Soit un groupe de Bianchi. Pour certains -modules , et suites de sous-groupes de congruence de nous démontrons une borne supérieure, conjecturée optimale, pour la taille du sous-groupe de torsion de l’homologie . On démontre aussi des résultats de multiplicités limites pour les facteurs irréductibles des espaces .
DOI: 10.5802/afst.1605
Mots-clés : Congruence groups, hyperbolic manifolds, homology
Jean Raimbault 1

@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}, mrnumber = {4014778}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1605/} }
TY - JOUR AU - Jean Raimbault TI - Analytic, Reidemeister and homological torsion for congruence three–manifolds JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 417 EP - 469 VL - 28 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1605/ DO - 10.5802/afst.1605 LA - en ID - AFST_2019_6_28_3_417_0 ER -
%0 Journal Article %A Jean Raimbault %T Analytic, Reidemeister and homological torsion for congruence three–manifolds %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 417-469 %V 28 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1605/ %R 10.5802/afst.1605 %G en %F AFST_2019_6_28_3_417_0
Jean Raimbault. Analytic, Reidemeister and homological torsion for congruence three–manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume spécial en l’honneur de Jean-Pierre OTAL “Low dimensional topology, hyperbolic manifolds and spectral geometry”, 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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