[Sur la -homologie équivariante de PSL sur les entiers quadratiques imaginaires]
Pour la -homologie équivariante de tous les groupes de Bianchi (PSL sur les entiers quadratiques imaginaires), nous démontrons des formules pour la partie due à la torsion, en termes de quantités élémentaires de la théorie des nombres. Pour arriver à cette fin, nous introduisons une nouvelle technique pour le calcul de l’homologie de Bredon : un scindage des anneaux de représentation, qui nous permet d’adapter la technique récente de réduction des sous-complexes de torsion, développée pour l’homologie des groupes, à notre usage pour l’homologie de Bredon.
We establish formulae for the part due to torsion of the equivariant -homology of all the Bianchi groups (PSL of the imaginary quadratic integers), in terms of elementary number-theoretic quantities. To achieve this, we introduce a novel technique in the computation of Bredon homology: representation ring splitting, which allows us to adapt the recent technique of torsion subcomplex reduction from group homology to Bredon homology.
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Keywords: Equivariant homology and cohomology, Equivariant $K$-theory, Bianchi groups, PSL$_2$ of the imaginary quadratic integers
Mot clés : Homologie et cohomologie équivariantes, $K$-théorie équivariante, Groupes de Bianchi, PSL$_2$ sur les entiers quadratiques imaginaires
Rahm, Alexander D. 1
@article{AIF_2016__66_4_1667_0,
author = {Rahm, Alexander D.},
title = {On the equivariant $K$-homology of {PSL}$_2$ of the imaginary quadratic integers},
journal = {Annales de l'Institut Fourier},
pages = {1667--1689},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {4},
year = {2016},
doi = {10.5802/aif.3047},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3047/}
}
TY - JOUR AU - Rahm, Alexander D. TI - On the equivariant $K$-homology of PSL$_2$ of the imaginary quadratic integers JO - Annales de l'Institut Fourier PY - 2016 SP - 1667 EP - 1689 VL - 66 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3047/ DO - 10.5802/aif.3047 LA - en ID - AIF_2016__66_4_1667_0 ER -
%0 Journal Article %A Rahm, Alexander D. %T On the equivariant $K$-homology of PSL$_2$ of the imaginary quadratic integers %J Annales de l'Institut Fourier %D 2016 %P 1667-1689 %V 66 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3047/ %R 10.5802/aif.3047 %G en %F AIF_2016__66_4_1667_0
Rahm, Alexander D. On the equivariant $K$-homology of PSL$_2$ of the imaginary quadratic integers. Annales de l'Institut Fourier, Tome 66 (2016) no. 4, pp. 1667-1689. doi : 10.5802/aif.3047. https://aif.centre-mersenne.org/articles/10.5802/aif.3047/
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