Erratum: Multiplicative stability for the cohomology of finite Chevalley groups. Math. Helvetici 63 (1988), 108-113.
We show that the homological dimension of a configuration space of a graph Γ is estimated from above by the number b of vertices in Γ whose valence is greater than 2. We show that this estimate is optimal for the n-point configuration space of Γ if n ≥ 2b.
Existence of proper Gorenstein projective resolutions and Tate cohomology is proved over rings with a dualizing complex. The proofs are based on Bousfield Localization which is originally a method from algebraic topology.
Complexes of groups over ordered simplicial complexes are generalizations to higher dimensions of graphs of groups. We first relate them to complexes of spaces by considering their classifying space . Then we develop their homological algebra aspects. We define the notions of homology and cohomology of a complex of groups with coefficients in a -module and show the existence of free resolutions. We apply those notions to study extensions of complexes of groups with constant or abelian kernel....