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Homology and K-theory of the Bianchi groups

Rahm, Alexander D.
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http://dx.doi.org/10.1016/j.crma.2011.05.014
 http://hdl.handle.net/10379/3834
 https://doi.org/10.13025/15270
Publication Date
2011
Keywords
K-homology, Bianchi groups, K-theory
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Article
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Rahm, Alexander D. (2011) 'Homology and K-theory of the Bianchi groups'. C. R. Math. Acad. Sci. Paris, 349 (11-12):615-619.
Abstract
We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group homology and equivariant K-homology. By the Baum/Connes conjecture, which holds for the Bianchi groups, we obtain the K-theory of their reduced C*-algebras in terms of isomorphic images of the computed K-homology. We further find an application to Chen/Ruan orbifold cohomology.
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Mathematics (Scholarly Articles)