Parametrized Kähler class and Zariski dense orbital 1-cohomology

Abstract

Let $\Gamma$ be a finitely generated group and let $(X,{\mu }_X)$ be an ergodic standard Borel probability $\Gamma$-space. Suppose that $G$ is the connected component of the identity of the isometry group of a Hermitian symmetric space. Given a Zariski dense measurable cocycle $\sigma :\Gamma \times X\to G$, we define the notion of parametrized Kähler class and we show that it completely determines the cocycle up to cohomology.x

arXiv comment24 pages, comments are welcome. Published in Mathematical Research Letters

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