Rational equivariant K-homology of low dimensional groups

Abstract

We consider groups G which have a cocompact, 3-manifold model for the classifying space \underline{E}G. We provide an algorithm for computing the rationalized equivariant K-homology of \underline{E}G. Under the additional hypothesis that the quotient 3-orbifold \underline{E}G/G is geometrizable, the rationalized K-homology groups coincide with the rationalized K-theory of the reduced C*-algebra of G. We illustrate our algorithm on some concrete examples.

32 pages, 5 figures

References in corpus (3)

• K- and L-theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by Z/4
• Lower algebraic K-theory of certain reflection groups
• The Lower Algebraic K-Theory of Split Three-Dimensional Crystallographic Groups

Cited by in corpus (1)

• Equivariant $K$-homology for hyperbolic reflection groups