On the equivariant K-homology of PSL 2 of the imaginary quadratic integers
Annales de l'Institut Fourier, Volume 66 (2016) no. 4, p. 1667-1689

We establish formulae for the part due to torsion of the equivariant K-homology of all the Bianchi groups (PSL 2 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.

Pour la K-homologie équivariante de tous les groupes de Bianchi (PSL 2 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.

Received : 2015-06-11
Revised : 2015-12-07
Accepted : 2016-01-21
Published online : 2016-07-28
DOI : https://doi.org/10.5802/aif.3047
Classification:  55N91,  19L47
Keywords: Equivariant homology and cohomology, Equivariant K-theory, Bianchi groups, PSL 2 of the imaginary quadratic integers
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {4},
     year = {2016},
     pages = {1667-1689},
     doi = {10.5802/aif.3047},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 66 (2016) no. 4, pp. 1667-1689. doi : 10.5802/aif.3047. http://www.numdam.org/item/AIF_2016__66_4_1667_0/

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