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 ۲. We give an interpretation of the first non-abelian cohomology of a topological group by the notion of a principle homogeneous space.

کلیدواژه ها:

Non-abelian cohomology of topological groups ، cocompatible triple ، partially crossed topological bimodule ، principle homogeneous space