[en] 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.
This means that we can complete previous computations with rational coefficients to get results with integral coefficients. On the way, we establish an efficient criterion for checking torsion-freeness of K-theory groups, which can be applied far beyond the scope of the present paper.
Disciplines :
Mathematics
Author, co-author :
Lafont, Jean-Francois; The Ohio State University
Ortiz, Ivonne; Miami University, Oxford, OH 45056, USA
RAHM, Alexander ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Sanchez-Garcia, Ruben; University of Southampton
External co-authors :
yes
Language :
English
Title :
Equivariant K-homology for hyperbolic reflection groups
Publication date :
01 December 2018
Journal title :
The Quarterly Journal of Mathematics
ISSN :
0033-5606
eISSN :
1464-3847
Publisher :
Oxford University Press, Oxford, United Kingdom
Volume :
69
Issue :
4
Pages :
1475-1505
Peer reviewed :
Peer reviewed
Funders :
Gabor Wiese’s University of Luxembourg grant AMFOR
