On Cohomology theory for topological groups

We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of identity. We show that if G and A are locally compact and seco...

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Bibliographic Details
Published inarXiv.org
Main Authors Khedekar, Arati S, Rajan, C S
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.09.2010
Subjects
Homology
Lie groups
Topology
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Summary:We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of identity. We show that if G and A are locally compact and second countable, then the second cohomology group based on locally continuous measurable cochains as above parametrizes the collection of locally split extensions of G by A.
ISSN:2331-8422