Bounded cohomology of transformation groups

Abstract

Let $M$ be a complete connected Riemannian manifold of finite volume. In this paper we present a new method of constructing classes in bounded cohomology of transformation groups such as $Home{o}_0(M,\mu )$, $Dif{f}_0(M,vol)$ and $Sym{p}_0(M,\omega )$ (in case $M$ is symplectic). As an application we show that, under certain conditions on ${\pi }_1(M)$, the $3^{rd}$ bounded cohomology of these groups is infinite dimensional.

arXiv comment19 pages, one figure; to appear in Mathematische Annalen