Let be a semidirect product of the form where is prime and the -action on is free away from the origin. We will compute the topological K-theory of the real and complex group C*-algebra of and show that 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 and . The latter is the quotient of the induced -action on the torus .
Cite this article
James F. Davis, Wolfgang Lück, The topological K-theory of certain crystallographic groups. J. Noncommut. Geom. 7 (2013), no. 2, pp. 373–431DOI 10.4171/JNCG/121