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Continuous bounded cohomology and applications to rigidity theory. (English) Zbl 1006.22010
The paper presents a theory of continuous bounded cohomology of locally compact groups with coefficients in Banach modules. The paper proves several results and we highlight some of them. Theorem 2: If \(G\) is a locally compact second countable group, \(S\) an amenable regular \(G\)-space and \(E\) a coefficient \(G\)-module, then the continuous bounded cohomology \(H^*_{cb} (G,E)\) is computed by the complex \[ 0\to L^\infty_{\omega^*} (S,E)^G\to L^\infty_{\omega^*} (S^2,E)^G\to \dots \] of bounded \(G\)-invariant cochains on \(S\).

MSC:
22E40 Discrete subgroups of Lie groups
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