Farrell Cohomology Theory

Abstract

Let Γ be a group such that vcd Γ < ∞. If Γ is torsion-free, then we know from Chapter VIII that cd Γ < ∞, so that Γ has no high-dimensional cohomology. In the general case, one might hope to “explain” the high-dimensional cohomology of Γ in terms of the torsion in Γ. (This is analogous to the situation of Chapter IX, where we tried to explain the non-integrality of χ(Γ) in terms of the torsion in Γ.)