Bounded cohomology and isometry groups of hyperbolic spaces | Zendy

Ursula Hamenstädt | Zendy

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Bounded cohomology and isometry groups of hyperbolic spaces

Author(s) -

Ursula Hamenstädt

Publication year - 2008

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/112

Subject(s) - mathematics , cohomology , bounded function , isometry (riemannian geometry) , pure mathematics , relatively hyperbolic group , hyperbolic group , mathematical analysis , hyperbolic manifold , hyperbolic function

Let X be an arbitrary hyperbolic geodesic metric space and let G be acountable non-elementary weakly acylindrical group of isometries of X. We showthat the second bounded cohomology group of G with real coefficients or withcoefficients in the regular representation is infinite dimensional. The resultholds for any subgroup of the mapping class group of a non-exceptional surfaceof finite type not containing a normal subgroup which virtually split as adirect product.

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