JournalsjncgVol. 7, No. 2pp. 373–431

The topological K-theory of certain crystallographic groups

  • James F. Davis

    Indiana University, Bloomington, USA
  • Wolfgang Lück

    University of Bonn, Germany
The topological K-theory of certain crystallographic groups cover

Abstract

Let Γ\Gamma be a semidirect product of the form ZnρZ/p\mathbb{Z}^n \rtimes_{\rho} \mathbb{Z}/p where pp is prime and the Z/p\mathbb{Z}/p-action ρ\rho on Zn\mathbb{Z}^n is free away from the origin. We will compute the topological K-theory of the real and complex group C*-algebra of Γ\Gamma and show that Γ\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 BGammaB Gamma and BΓ\underline{B} \Gamma. The latter is the quotient of the induced Z/p\mathbb{Z}/p-action on the torus TnT^n.

Cite this article

James F. Davis, Wolfgang Lück, The topological K-theory of certain crystallographic groups. J. Noncommut. Geom. 7 (2013), no. 2, pp. 373–431

DOI 10.4171/JNCG/121