Continuous Bounded Cohomology of Locally Compact Groups

1. Front Matter

   Pages I-IX

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2. Introduction

   Pages 1-7

3. Banach modules, L∞ spaces

   Pages 9-30

4. Relative injectivity and amenable actions

   Pages 31-60

5. Definition and characterization of continuous bounded cohomology

   Pages 61-127

6. Cohomological techniques

   Pages 129-168

7. Towards applications

   Pages 169-201

8. Back Matter

   Pages 203-214

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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.

• Bounded cohomology
• Cohomology
• Lattice
• continuous cohomology
• homology
• lattices in Lie groups
• rigidity theory

• Department of Mathematics, ETH-Zürich, Zürich, Switzerland

  Nicolas Monod

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