Bounded Cohomology, Boundary Maps, and Rigidity of Representations into Homeo+(S1) and SU(1, n)

  • Alessandra Iozzi


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].


Cohomology Class Euler Number Order Preserve Euler Class Amenable Action 
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© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alessandra Iozzi
    • 1
  1. 1.ETH ZentrumZürichSwitzerland

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