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arXiv · 1407.5071

First Non-abelian Cohomology of Topological Groups II

Hossein Sahleh·Hossein Esmaili Koshkoshi
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Abstract

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.

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Hossein Sahleh, Hossein Esmaili Koshkoshi. 2014-07-18. First Non-abelian Cohomology of Topological Groups II. https://arxiv.org/abs/1407.5071

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