The topological K-theory of certain crystallographic groups

Details The topological K-theory of certain crystallographic groups The topological K-theory of certain crystallographic groups

2010-04-15

arxiv.org/abs/1004.2660v2

Mathematics

K-Theory and Homology

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

Scientific paper

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.

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