The topological Ktheory 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/paction on Z^n is free away from the origin. We will compute the topological Ktheory of the real and complex group C*algebra of Gamma and show that Gamma satisfies the unstable GromovLawsonRosenberg Conjecture. On the way we will analyze the (co)homology and the topological Ktheory of the classifying spaces BGamma and underbar{B}Gamma. The latter is the quotient of the induced Z/paction on the torus T^n.
 Publication:

arXiv eprints
 Pub Date:
 April 2010
 arXiv:
 arXiv:1004.2660
 Bibcode:
 2010arXiv1004.2660D
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Algebraic Topology;
 Mathematics  Geometric Topology;
 19L47;
 46L80;
 53C21
 EPrint:
 46 pages. Final version. Accepted for publication in the Journal of Noncommutative Geometry