Symmetric continuous cohomology of topological groups
Group Theory
2013-06-04 v3 General Topology
Abstract
In this paper, we introduce a symmetric continuous cohomology of topological groups. This is obtained by topologizing a recent construction due to Staic (J. Algebra 322 (2009), 1360-1378), where a symmetric cohomology of abstract groups is constructed. We give a characterization of topological group extensions that correspond to elements of the second symmetric continuous cohomology. We also show that the symmetric continuous cohomology of a profinite group with coefficients in a discrete module is equal to the direct limit of the symmetric cohomology of finite groups. In the end, we also define symmetric smooth cohomology of Lie groups and prove similar results.
Keywords
Cite
@article{arxiv.1105.5218,
title = {Symmetric continuous cohomology of topological groups},
author = {Mahender Singh},
journal= {arXiv preprint arXiv:1105.5218},
year = {2013}
}
Comments
23 pages, to appear in Homology Homotopy and Applications