Cohomology theory in topological groups.

Topological Methods in Abstract Algebra. Cohomology Theory of 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...

Cohomology Theory of Abelian Groups

This note will present certain algebraic results obtained by Samuel Eilenberg and the author in a study of the relations between homotopy and homology groups of a topological space. These results yield a homology theory for any abelian group II, in which the low dimensional homology and cohomology groups of n correspond to familiar constructions on II. They depend upon the application of the me...

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...

Cohomology of topological groups with applications to the Weil group

We establish various properties of the definition of cohomology of topological groups given by Grothendieck, Artin and Verdier in SGA4, including a Hochschild-Serre spectral sequence and a continuity theorem for compact groups. We use these properties to compute the cohomology of the Weil group of a totally imaginary field, and of the Weil-étale topology of a number ring recently introduced by ...