# Finite reducibility of maximal infinite dimensional measurable cocycles of complex hyperbolic lattices

@article{Sarti2020FiniteRO, title={Finite reducibility of maximal infinite dimensional measurable cocycles of complex hyperbolic lattices}, author={Filippo Sarti and Alessio Savini}, journal={arXiv: Geometric Topology}, year={2020} }

Given $\Gamma < \text{PU}(n,1)$ a torsion-free lattice and $(X,\mu_X)$ a standard Borel $\Gamma$-space, we introduce the notion of Toledo invariant of a measurable cocycle $\sigma:\Gamma \times X \rightarrow \text{PU}(p,\infty)$. Since that invariant has bounded absolute value, it makes sense to speak about maximality. We prove that any maximal measurable cocycle is finitely reducible, that is it admits a cohomologous cocycle with image contained in a copy of $\text{PU}(p,np)$ inside $\text{PU… CONTINUE READING

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