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arXiv · 2205.03653

On the trivializability of rank-one cocycles with an invariant field of projective measures

Alessio Savini
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Abstract

Let $G$ be $\text{SO}^\circ(n,1)$ for $n \geq 3$ and consider a lattice $Γ< G$. Given a standard Borel probability $Γ$-space $(Ω,μ)$, consider a measurable cocycle $σ:Γ\times Ω\rightarrow \mathbf{H}(κ)$, where $\mathbf{H}$ is a connected algebraic $κ$-group over a local field $κ$. Under the assumption of compatibility between $G$ and the pair $(\mathbf{H},κ)$, we show that if $σ$ admits an equivariant field of probability measures on a suitable projective space, then $σ$ is trivializable. An analogous result holds in the complex hyperbolic case.

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Alessio Savini. 2023-12-08. On the trivializability of rank-one cocycles with an invariant field of projective measures. https://arxiv.org/abs/2205.03653

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