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

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 $\Gamma$ 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 $\Gamma$.

References in corpus (2)

• Segal's spectral sequence in twisted equivariant K-theory for proper and discrete actions
• The Lower Algebraic K-Theory of Split Three-Dimensional Crystallographic Groups

Cited by in corpus (1)

• A Kunneth formula for Bredon cohomology of pullbacks and twisted K-theory of some 6-dimensional orbifolds