Bounded cohomology, boundary maps, and rigidity of representations into \(\text{Homeo}_+(\text{S}^1)\) and \(\text{SU}(1,n)\). (English) Zbl 1012.22023

Iozzi, Alessandra

Burger, Marc (ed.) et al., Rigidity in dynamics and geometry. Contributions from the programme Ergodic theory, geometric rigidity and number theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, UK, January 5-July 7, 2000. Berlin: Springer. 237-260 (2002).

The author defines invariants associated to a representation \(\pi:\Gamma\to H\), where \(\Gamma\) is a finitely generated group and \(H\) is a topological group, via the interplay between the pull-backs of bounded cohomology classes and ordinary cohomology classes of \(H\). It should be noted that the idea of considering what information one can obtain by looking at cohomology classes which admit a bounded representative as bounded cohomology classes is certainly not new. The point that the author makes here is that extra information can be obtained by considering a functorial approach to (continuous) bounded cohomology.
For the entire collection see [Zbl 0987.00036].

Reviewer: Messoud Efendiev (Berlin)

MSC:

22E41

Continuous cohomology of Lie groups

Keywords:

cohomology classes; functorial approach; bounded cohomology