FIRST NON-ABELIAN COHOMOLOGY OF TOPOLOGICAL GROUPS II

In this paper we introduce a new denition of the rst 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 in ation- restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the rst non-abelian cohomology of a topological group by the notion of a principle homogeneous space.