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See detailEquivariant K-homology for hyperbolic reflection groups
Lafont, Jean-Francois; Ortiz, Ivonne; Rahm, Alexander UL et al

in The Quarterly Journal of Mathematics (2018), 69(4), 1475-1505

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 ... [more ▼]

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. [less ▲]

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