Equivariant K-homology for hyperbolic reflection groups
Equivariant K-homology for hyperbolic reflection groups
We compute the equivariant K-homology of the classifying space for proper actions, for cocompact 3-dimensional hyperbolic reflection groups. This coincides with the topological K-theory of the reduced C∗-algebra associated to the group, via the Baum-Connes conjecture. We show that, for any such reflection group, the associated K-theory groups are torsion-free. As a result we can promote previous rational computations to integral computations. Our proof relies on a new efficient algebraic criterion for checking torsion-freeness of K-theory groups, which could be applied to many other classes of groups.
1475-1505
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Lafont, Jean-Francois
5de98a71-0130-43c5-b069-bbcb6f5d8b87
Ortiz, Ivonne
4c5e3b29-43aa-43b8-b163-254a91862480
Rham, Alexander
8a2577d2-f1e7-453c-a58e-1bb00488e93d
December 2018
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Lafont, Jean-Francois
5de98a71-0130-43c5-b069-bbcb6f5d8b87
Ortiz, Ivonne
4c5e3b29-43aa-43b8-b163-254a91862480
Rham, Alexander
8a2577d2-f1e7-453c-a58e-1bb00488e93d
Sanchez Garcia, Ruben, Lafont, Jean-Francois, Ortiz, Ivonne and Rham, Alexander
(2018)
Equivariant K-homology for hyperbolic reflection groups.
The Quarterly Journal of Mathematics, .
(doi:10.1093/qmath/hay030).
Abstract
We compute the equivariant K-homology of the classifying space for proper actions, for cocompact 3-dimensional hyperbolic reflection groups. This coincides with the topological K-theory of the reduced C∗-algebra associated to the group, via the Baum-Connes conjecture. We show that, for any such reflection group, the associated K-theory groups are torsion-free. As a result we can promote previous rational computations to integral computations. Our proof relies on a new efficient algebraic criterion for checking torsion-freeness of K-theory groups, which could be applied to many other classes of groups.
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Lafont_Ortiz_Rahm_Sanchez-Garcia
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Lafont_Ortiz_Rahm_Sanchez-Garcia_accepted
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Accepted/In Press date: 11 May 2018
e-pub ahead of print date: 13 July 2018
Published date: December 2018
Identifiers
Local EPrints ID: 415210
URI: http://eprints.soton.ac.uk/id/eprint/415210
ISSN: 0033-5606
PURE UUID: deb8f0e7-e8c0-4f12-8e55-e7fec6c69f2b
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Date deposited: 02 Nov 2017 17:30
Last modified: 16 Mar 2024 05:52
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Author:
Jean-Francois Lafont
Author:
Ivonne Ortiz
Author:
Alexander Rham
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