Geodesic
Symmetric continuous cohomology of topological groups
Homology, homotopy, and applications, Tome 15 (2013) no. 1, pp. 279-302.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2013.v15.n1.a14
Classification : 20J06, 54H11, 57T10
Keywords: continuous cohomology, group extension, Lie group, profinite group, symmetric cohomology, topological group 
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     pages = {279--302},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n1.a14/}
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Mahender Singh. Symmetric continuous cohomology of topological groups. Homology, homotopy, and applications, Tome 15 (2013) no. 1, pp. 279-302. doi : 10.4310/HHA.2013.v15.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n1.a14/

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