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

Alexander D. Rahm (1)

1 NUIG - Department of Mathematics

We establish formulae for the torsion part 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. 2015. ⟨hal-01162857v1⟩