Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduc...

Let A be a Banach algebra. A is called ideally amenable if for every closed ideal I of A, the first cohomology group of A with coefficients in I* is trivial. We investigate the closed ideals I for which H1 (A,I* )={0}, whenever A is weakly amenable or a biflat Banach algebra. Also we give some hereditary properties of ideal amenability.

1 Equivariant Cohomology 1 1.1 Group cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Equivariant cohomology of topological spaces . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Equivariant vector bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Equivariant pushforward . . . . . . . . . . . . . . . . . . . . . . . ....

We show that Haefliger’s cohomology for étale groupoids, Moore’s cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (or Čech) cohomology for topological simplicial spaces.

The aim of this thesis is to study profinite groups of type FPn. These are groups G which admit a projective resolution P of Ẑ as a ẐJGK-module such that P0, . . . , Pn are finitely generated, so this property can be studied using the tools of profinite group cohomology. In studying profinite groups it is often useful to consider their cohomology groups with profinite coefficients, but pre-exis...

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we have a group with infinitely many ends has infinite dimensional second bounded cohomology.

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we show that a group with infinitely many ends has infinite dimensional second bounded cohomology.

Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F-projective resolution for Z when F is the family of all subgroups H ≤ G with rkH ≤ rkG − 1. We answer this question negatively by calculating the relative group cohomology FH(G,F2) where G = Z/2 × Z/2 and F is the family o...