#### Volume 14, issue 2 (2014)

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Twisted equivariant $K\!$–theory and $K\!$–homology of $\mathrm{Sl}_3{\mathbb{Z}}$

### Noé Bárcenas and Mario Velásquez

Algebraic & Geometric Topology 14 (2014) 823–852
##### Abstract

We use a spectral sequence to compute twisted equivariant $K\phantom{\rule{0.3em}{0ex}}$–theory groups for the classifying space of proper actions of discrete groups. We study a form of Poincaré duality for twisted equivariant $K\phantom{\rule{0.3em}{0ex}}$–theory studied by Echterhoff, Emerson and Kim in the context of the Baum–Connes conjecture with coefficients and verify it for the group ${Sl}_{3}\left(ℤ\right)$.

##### Keywords
universal coefficient theorem, Bredon cohomology, twisted $K$–theory, Baum–Connes conjecture with coefficients, twisted equivariant $k$–theory, twisted group $C^*$–algebras, $\mathit{KK}$–theoretic duality
##### Mathematical Subject Classification 2010
Primary: 19L47
Secondary: 55N91, 46L80