Cohomology of fibre spaces with group bundle coefficients

The Cohomology of a Coxeter Group with Group Ring Coefficients

Cohomology with Chains as Coefficients

THE cohomology theory described in the title is obtained by replacing the usual coefficient group by an arbitrary chain complex. This theory satisfies all of the Eilenberg-Steenrod axioms for a cohomology theory except the dimension axiom. There are other theories with this property, and among these our theory is probably the least extraordinary. That is to say, its definition and techniques ar...

Cohomology with Grosshans graded coefficients

Let the reductive group G act on the finitely generated commutative k-algebra A. We ask if the finite generation property of the ring of invariants extends to the full cohomology ring. We confirm this when the action on A is replaced by the ‘contracted’ action on the Grosshans graded ring grA, provided the characteristic of k is large.

Equivariant Cohomology with Local Coefficients

We show that for a discrete group G, the equivariant cohomology of a G-space X with G-local coefficients M is isomorphic to the Bredon-Iliman cohomology of X with equivariant local coefficients M.

Cohomology of Coxeter groupswith group ring coefficients: II

The cohomology of a group G with coefficients in a left G–module M is denoted H .GIM /. We are primarily interested in the case where M is the group ring, ZG . Since ZG is a G–bimodule, H .GIZG/ inherits the structure of a right G– module. When G is discrete and acts properly and cocompactly on a contractible CW complex , there is a natural topological interpretation for this cohomology group:...