Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First Non-Abelian Cohomology of Topological Groups   Let $G$ be a topological group and $A$ a topological $G$-module (not
necessarily abelian). In this paper, we define $H^{0}(G,A)$ and $H^{1}(G,A)$
and will find a six terms exact cohomology sequence involving $H^{0}$ and
$H^{1}$. We will extend it to a seven terms exact sequence of cohomology up to
dimension two. We find a criterion such that vanishing of $H^{1}(G,A)$ implies
the connectivity of $G$. We show that if $H^{1}(G,A)=1$, then all complements
of $A$ in the semidirect product $G\ltimes A$ are conjugate. Also as a result,
we prove that if $G$ is a compact Hausdorff group and $A$ is a locally compact
almost connected Hausdorff group with the trivial maximal compact subgroup
then, $H^{1}(G,A)=1$.

5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ