# The topological K-theory of certain crystallographic groups - Mathematics > K-Theory and Homology

The topological K-theory of certain crystallographic groups - Mathematics > K-Theory and Homology - Download this document for free, or read online. Document in PDF available to download.

Abstract: Let Gamma be a semidirect product of the form Z^n rtimes Z-p where p is primeand the Z-p-action on Z^n is free away from the origin. We will compute thetopological K-theory of the real and complex group C*-algebra of Gamma and showthat Gamma satisfies the unstable Gromov-Lawson-Rosenberg Conjecture. On theway we will analyze the co-homology and the topological K-theory of theclassifying spaces BGamma and underbar{B}Gamma. The latter is the quotient ofthe induced Z-p-action on the torus T^n.

Author: ** James F. Davis, Wolfgang Lueck**

Source: https://arxiv.org/