MOD-2 (CO)homology of an Abelian Group

Mod 2 Cohomology of Combinatorial Grassmannians

Oriented matroids have long been of use in various areas of combinatorics [BLS93]. Gelfand and MacPherson [GM92] initiated the use of oriented matroids in manifold and bundle theory, using them to formulate a combinatorial formula for the rational Pontrjagin classes of a differentiable manifold. MacPherson [Mac93] abstracted this into a manifold theory (combinatorial differential (CD) manifolds...

The Mod-2 Cohomology of the Bianchi Groups

The Bianchi groups are a family of discrete subgroups of PSL2(C) which have group theoretic descriptions as amalgamated products and HNN extensions. Using Bass-Serre theory, we show how the cohomology of these two constructions relates to the cohomology of their pieces. We then apply these results to calculate the mod-2 cohomology ring for various Bianchi groups.

First non-abelian cohomology of topological groups II

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

On the cohomology of discrete abelian group actions

Generalizing a result of Depauw, we prove that the geometric cohomology groups for a Z d action are in any dimension isomorphic to the Feldman-Moore cohomology groups rsp. the algebraic group cohomology groups. This result holds in the smooth, topological or measurable category and for general Polish groups as coeecient groups.

Mod Two Homology and Cohomology