The topological K-theory of certain crystallographic groups
K-Theory and Homology
2015-11-30 v2 Algebraic Topology
Geometric Topology
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.
Keywords
Cite
@article{arxiv.1004.2660,
title = {The topological K-theory of certain crystallographic groups},
author = {James F. Davis and Wolfgang Lueck},
journal= {arXiv preprint arXiv:1004.2660},
year = {2015}
}
Comments
46 pages. Final version. Accepted for publication in the Journal of Noncommutative Geometry