The topological K-theory of certain crystallographic groups

Abstract

Let Gamma be a semidirect product of the form Z^n rtimes Z/p where p is prime and the Z/p-action on Z^n is free away from the origin. We will compute the topological K-theory of the real and complex group C*-algebra of Gamma and show that Gamma satisfies the unstable Gromov-Lawson-Rosenberg Conjecture. On the way we will analyze the (co-)homology and the topological K-theory of the classifying spaces BGamma and underbar{B}Gamma. The latter is the quotient of the induced Z/p-action on the torus T^n.

46 pages. Final version. Accepted for publication in the Journal of Noncommutative Geometry

References in corpus (1)

• Topological K-(co-)homology of classifying spaces of discrete groups

Cited by in corpus (4)

• Twisted crystallograpic T-duality via the Baum--Connes isomorphism
• On the equivariant $K$- and $KO$-homology of some special linear groups
• Equivariant $K$-homology for hyperbolic reflection groups
• Manifolds homotopy equivalent to certain torus bundles over lens spaces