On Cohomology theory for topological groups

Details On Cohomology theory for topological groups On Cohomology theory for topological groups

2010-09-23

arxiv.org/abs/1009.4519v1

Mathematics

General Topology

27 pages

Scientific paper

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.

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