Continuous Bounded Cohomology of Locally Compact Groups

Nicolas Monod (eds.)3540420541, 9783540420545

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.

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Table of contents :
Introduction….Pages 1-7
Banach modules, L ∞ spaces….Pages 9-30
Relative injectivity and amenable actions….Pages 31-60
Definition and characterization of continuous bounded cohomology….Pages 61-127
Cohomological techniques….Pages 129-168
Towards applications….Pages 169-201