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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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–theory groups for the classifying space of proper actions of discrete groups. We study a form of Poincaré duality for twisted equivariant K–theory studied by Echterhoff, Emerson and Kim in the context of the Baum–Connes conjecture with coefficients and verify it for the group Sl3().

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
References
Publication
Received: 3 April 2013
Revised: 19 August 2013
Accepted: 10 September 2013
Published: 31 January 2014
Authors
Noé Bárcenas
Centro de Ciencias Matemáticas
UNAM Campus Morelia, Michoacán
Ap. Postal 61-3 Xangari
58089 Morelia
Mexico
http://www.matmor.unam.mx/~barcenas
Mario Velásquez
Centro de Ciencias Matemáticas
UNAM Campus Morelia, Michoacán
Ap. Postal 61-3 Xangari
58089 Morelia
Mexico