On the equivariant K-homology of PSL_2 of the imaginary quadratic integers

Alexander D. Rahm (1)

1 FSTC - Faculty of Science, Technology and Communication [Luxembourg]

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.

Domaines: K-théorie et homologie [math.KT]

Alexander D. Rahm. On the equivariant K-homology of PSL_2 of the imaginary quadratic integers. Annales de l'Institut Fourier, 2016, (accepted for publication on January 21, 2016). ⟨hal-01162857v2⟩