- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:13
Journal of Noncommutative Geometry
J. Noncommut. Geom.
JNCG
1661-6952
1661-6960
Global analysis, analysis on manifolds
General
10.4171/JNCG
http://www.ems-ph.org/doi/10.4171/JNCG
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2013
2
The topological K-theory of certain crystallographic groups
James
Davis
Indiana University, BLOOMINGTON, UNITED STATES
Wolfgang
Lück
Universität Bonn, BONN, GERMANY
Group homology, topological K-theory, (unstable) Gromov–Lawson–Rosenberg Conjecture, extensions of $\mathbb{Z}^n$ by $\mathbb{Z}/p$
Let $\Gamma$ be a semidirect product of the form $\mathbb{Z}^n \rtimes_{\rho} \mathbb{Z}/p$ where $p$ is prime and the $\mathbb{Z}/p$-action $\rho$ on $\mathbb{Z}^n$ 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 $B Gamma$ and $\underline{B} \Gamma$. The latter is the quotient of the induced $\mathbb{Z}/p$-action on the torus $T^n$.
$K$-theory
Functional analysis
Differential geometry
General
373
431
10.4171/JNCG/121
http://www.ems-ph.org/doi/10.4171/JNCG/121