Let M be a complete connected Riemannian manifold of finite volume. We present a new method of constructing classes in bounded cohomology of transformation groups such as Homeo (M, μ) , Diff (M, vol) and Symp (M, ω). As an application we show that for many manifolds (in particular for hyperbolic surfaces) the third bounded cohomology of these groups is infinite dimensional.
ASJC Scopus subject areas
- Mathematics (all)