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arXiv · 1311.3138

Bredon Cohomology, K theory and K homology of Pullbacks of groups

Noe Barcenas·Daniel Juan-Pineda·Mario Velasquez
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Abstract

We develop an Eilenberg-Moore spectral sequence to compute Bredon cohomology of spaces with an action of a group given as a pullback. Using several other spectral sequences, and positive results on the Baum-Connes Conjecture, we are able to compute Equivariant K-theory and K-Homology of the reduced group C*-algebra of a 6-dimensional crystallographic group $Γ$ introduced by Vafa and Witten. We also use positive results on the Farrell-Jones Conjecture to give a vanishing result for the negative algebraic K-theory of the integral group ring of $Γ$.

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Noe Barcenas, Daniel Juan-Pineda, Mario Velasquez. 2014-08-18. Bredon Cohomology, K theory and K homology of Pullbacks of groups. https://arxiv.org/abs/1311.3138

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