Let Γ be a finitely generated group and let (X, µX ) be an ergodic standard Borel probability Γ-space. Suppose that X is a Hermitian symmetric space not of tube type and assume that G = Isom(X)◦ is simple. Given a Zariski dense measurable cocycle σ: Γ × X → G, we define the notion of parametrized Kähler class and we show that it completely determines the cocycle up to cohomology.
Sarti, F., Savini, A. (2023). Parametrized Kähler class and Zariski dense orbital 1-cohomology. MATHEMATICAL RESEARCH LETTERS, 30(6), 1895-1929 [10.4310/MRL.2023.v30.n6.a9].
Parametrized Kähler class and Zariski dense orbital 1-cohomology
Savini A.
2023
Abstract
Let Γ be a finitely generated group and let (X, µX ) be an ergodic standard Borel probability Γ-space. Suppose that X is a Hermitian symmetric space not of tube type and assume that G = Isom(X)◦ is simple. Given a Zariski dense measurable cocycle σ: Γ × X → G, we define the notion of parametrized Kähler class and we show that it completely determines the cocycle up to cohomology.
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