Corpus ID: 218763416

# 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}
}
• Published 2020
• Mathematics
• arXiv: Geometric Topology
• 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 #### References ##### Publications referenced by this paper. SHOWING 1-10 OF 35 REFERENCES ## Superrigidity of maximal measurable cocycles of complex hyperbolic lattices • Mathematics • 2020 ## Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups ## A Matsumoto-Mostow result for Zimmer's cocycles of hyperbolic lattices • Mathematics • 2019 ## Bounded differential forms, generalized Milnor–Wood inequality and an application to deformation rigidity • Mathematics • 2007 ## Borel invariant for Zimmer cocycles of 3-manifold groups ## The bounded Borel class and$3\$-manifold groups

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