%0 Journal Article %T First non-abelian cohomology of topological groups II %J Journal of Algebra and Related Topics %I University of Guilan %Z 2345-3931 %A Sahleh, H. %A Koshkoshi, H. E. %D 2014 %\ 12/01/2014 %V 2 %N 2 %P 43-61 %! First non-abelian cohomology of topological groups II %K Non-abelian cohomology of topological groups %K cocompatible triple %K partially crossed topological bimodule %K principle homogeneous space %R %X 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-abelian cohomology of a topological group by the notion of a principle homogeneous space. %U https://jart.guilan.ac.ir/article_66_401debc98c625ef131a511bc9335c425.pdf