Standard Projective Simplicial Kernels and the Second Abelian Cohomology of Topological Groups

Hossein Sahleh; Hossein Esmaili Koshkoshi

Standard Projective Simplicial Kernels and the Second Abelian Cohomology of Topological Groups

Group Theory 2015-02-10 v1 General Topology

Authors: Hossein Sahleh , Hossein Esmaili Koshkoshi

Abstract

Let $A$ be an abelian topological $G$ -module. We give an interpretion for the second cohomology, $H^{2}(G,A)$ , of $G$ with coefficients in $A$ . As a result we show that if $P$ is a projective topological group, then $H^{2}(P,A)=0$ for every abelian topological $P$ -module $A$ .

Keywords

topological group abelian topological module second cohomology projective topological group simplicial kernel group cohomology standard projective simplicial kernel

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@article{arxiv.1502.02237,
  title  = {Standard Projective Simplicial Kernels and the Second Abelian Cohomology of Topological Groups},
  author = {Hossein Sahleh and Hossein Esmaili Koshkoshi},
  journal= {arXiv preprint arXiv:1502.02237},
  year   = {2015}
}

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12 pages

Standard Projective Simplicial Kernels and the Second Abelian Cohomology of Topological Groups

Abstract

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