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

Alessandra Iozzi ()
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Alessandra Iozzi: ETH Zentrum

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 237-260 from Springer

Abstract: 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].

Keywords: Cohomology Class; Euler Number; Order Preserve; Euler Class; Amenable Action (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-3-662-04743-9_12

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