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

Rahm, Alexander D.
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Publication Date
2016-09
Keywords
Equivariant homology and cohomology, Equivariant K-theory, Bianchi groups, PSL(2) of the imaginary quadratic integers
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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 .
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.
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|~|
Publisher
Association des Annales de l'Institut Fourier
Publisher DOI
10.5802/aif.3047
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Mathematics (Scholarly Articles)