# Continuous bounded cohomology of locally compact groups

@inproceedings{Ducimetire2000ContinuousBC, title={Continuous bounded cohomology of locally compact groups}, author={Nicolas Ducimeti{\`e}re}, year={2000} }

We introduce and study the theory of continuous bounded cohomology of topological groups with coefficients in Banach modules. This encompasses the bounded cohomology of abstract groups as a special case ;ourmainresultsarealsonewinthissetting.Certaintechniques,suchasinductionandspectralsequences,arein¬spiredbyclassicalcohomology.Othersarespecifictothisnewtheory:thisisthecaseoftheuseofamenableactionsanddoubleergodicitywithcoefficients…

## 103 Citations

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A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is…

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We use cross ratios to describe second real continuous bounded cohomology for locally compact topological groups. We also derive a rigidity result for cocycles with values in the isometry group of a…

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Abstract We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups.…

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We present a new technique that employs partial dierential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As an application, we prove a…

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