Bounded Cohomology, Boundary Maps, and Rigidity of Representations into Homeo+(S1) and SU(1, n)
We define, associated to a given a representation π: Γ → H of a finitely generated group into a topological group, invariants defined in terms of bounded cohomology classes. In the case H = SU(1, n) we illustrate, among others and without proof, rigidity results which generalize a theorem of Goldman and Millson (). In the case H = Homeo+(S1), the group of orientation preserving homeomorphisms of the circle, we give a new complete proof of a rigidity result of Matsumoto (), stating that any two representations with maximal Euler number are semiconjugate.
The methods used rely on the homological approach to continuous bounded cohomology developed in and .
KeywordsCohomology Class Euler Number Order Preserve Euler Class Amenable Action
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