Homology and K-theory of the Bianchi groups
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2011Author
Rahm, Alexander D.
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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.
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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.