Abstract
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 ([14]). 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 ([17]), 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 [5]and [1].
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Iozzi, A. (2002). Bounded Cohomology, Boundary Maps, and Rigidity of Representations into Homeo+(S1) and SU(1, n). In: Burger, M., Iozzi, A. (eds) Rigidity in Dynamics and Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04743-9_12
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DOI: https://doi.org/10.1007/978-3-662-04743-9_12
Publisher Name: Springer, Berlin, Heidelberg
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