Homology, Homotopy and Applications

Symmetric continuous cohomology of topological groups

Mahender Singh

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Abstract

In this paper, we introduce a symmetric continuous cohomology of topological groups. This is obtained by topologizing a recent construction due to Staic, 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.

Article information

Source
Homology Homotopy Appl., Volume 15, Number 1 (2013), 279-302.

Dates
First available in Project Euclid: 8 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hha/1383943678

Mathematical Reviews number (MathSciNet)
MR3079208

Zentralblatt MATH identifier
1275.22010

Subjects
Primary: 20J06: Cohomology of groups
Secondary: 54H11: Topological groups [See also 22A05] 57T10: Homology and cohomology of Lie groups

Keywords
Continuous cohomology group extension Lie group profinite group symmetric cohomology topological group

Citation

Singh, Mahender. Symmetric continuous cohomology of topological groups. Homology Homotopy Appl. 15 (2013), no. 1, 279--302. https://projecteuclid.org/euclid.hha/1383943678


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