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 Teichm ller spaces. A special effort has been made to
provide detailed proofs or references in quite some generality.
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