On the equivariant K-homology of PSL_2 of the imaginary quadratic integers
Rahm, Alexander D.
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Rahm, Alexander D. (2016) 'On the equivariant K-homology of PSL_2 of the imaginary quadratic integers'. Annales De L Institut Fourier, (66) 4 pp. 1667-89 .
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.