On the equivariant K-homology of PSL\_2 of the imaginary quadratic integers

Abstract

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.

arXiv commentAnnales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2016, (accepted for publication on January 21, 2016)