A. Savini

activity

20152026

most citedSuperrigidity of maximal measurable cocycles of complex hyperbolic lattices

11 citations · 59 across the 31 of their papers we have counts for

collaborators

32 papers

math.DS2026

Similarity and superrigidity for transverse measured groupoids

Filippo Sarti, Alessio Savini

Let $G$ be a locally compact, second countable, unimodular group and let $(X, μ, Y)$ be an ergodic integrable transverse $G$ -system. We show that $G ⋉ X$ endowed with the produ…

math.OA2025

Uniformly bounded representations of discrete measured groupoid into finite Von Neumann algebras

Alessio Savini

Let $(G, ν)$ be a $t$ -discrete ergodic groupoid. Consider a finite Von Neumann algebra $M$ with separable predual. We prove that every uniformly bounded measurab…

math.GR2025

Continuous cochains on Furstenberg boundaries and injectivity of the comparison map

Michelle Bucher, Alessio Savini

Monod proved that any continuous cohomology of a semisimple Lie group $G$ can be represented by a measurable cocycle on the associated Furstenberg boundary, which we upgraded to an…

math.GR2025

Projections from Furstenberg boundaries onto maximal flats and barycenter maps

Michelle Bucher, Alessio Savini

Let $G$ be a semisimple connected Lie group of non-compact type with finite center. Let $K < G$ be a maximal compact subgroup and $P < G$ be a minimal parabolic subgroup. For any pair…

math.AT2025

Measurable bounded cohomology of $t$ -discrete measured groupoids via resolutions

Filippo Sarti, Alessio Savini

We define bounded cohomology of $t$ -discrete measured groupoids with coefficients into measurable bundles of Banach spaces. Our approach via homological algebra extends the classic…

math.DS2024

Boundaries and equivariant maps for ergodic groupoids

Filippo Sarti, Alessio Savini

We give a notion of boundary pair $(B_{-}, B_{+})$ for measured groupoids which generalizes the one introduced by Bader and Furman \cite{BF14} for locally compact gr…

math.GR2023

Kernels in measurable cohomology for transitive actions

Michelle Bucher, Alessio Savini

Given a connected semisimple Lie group $G$ , Monod has recently proved that the measurable cohomology of the $G$ -action $H_{m}^{*} (G ↷ G / P)$ on the Furstenberg boundary $…

math.GR2023

Alternating cochains on Furstenberg boundaries and measurable cohomology

Michelle Bucher, Alessio Savini

Nicolas Monod showed that the evaluation map $H_{m}^{*} (G ↷ G / P) ⟶ H_{m}^{*} (G)$ between the measurable cohomology of the action of a connected semisimple Lie…

math.DS2023

Measurable bounded cohomology of measured groupoids

Filippo Sarti, Alessio Savini

We introduce the notion of measurable bounded cohomology for measured groupoids, extending continuous bounded cohomology of locally compact groups. We show that the measurable boun…

math.GT2022★ 2 cited

Bounded Cohomology Classes of Exact Forms

Ludovico Battista, Stefano Francaviglia, Marco Moraschini +2

On negatively curved compact manifolds, it is possible to associate to every closed form a bounded cocycle - hence a bounded cohomology class - via integration over straight simpli…

math.DS2022

Orbital cohomology and Kahler rigidity

Alessio Savini

In the late $70$ 's Feldman and Moore defined the cohomology associated to a countable equivalence relation with coefficients in an Abelian Polish group. When the equivalence relati…

math.GR2022

Some explicit cocycles on the Furstenberg boundary for products of isometries of hyperbolic spaces and $SL (3, K)$

Michelle Bucher, Alessio Savini

Nicolas Monod showed that the evaluation map $H_{m}^{*} (G ↷ G / P) ⟶ H_{m}^{*} (G)$ between the measurable cohomology of the action of a connected semisimple Lie gr…

math.DS2022

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

Alessio Savini

Let $G$ be $SO^{\circ} (n, 1)$ 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\rig…

math.DS2021

A Note on elementarity of virtual dendro-morphisms for higher rank lattices

Alessio Savini

Let $Γ$ be a discrete countable group and let $(Ω, μ)$ be an ergodic standard Borel probability $Γ$ -space. Given any non-elementary virtual dendro-morphism (that is a measurable coc…

math.GT2021★ 2 cited

Parametrized Kähler class and Zariski dense orbital 1-cohomology

Filippo Sarti, Alessio Savini

Let $Γ$ be a finitely generated group and let $(X, μ_{X})$ be an ergodic standard Borel probability $Γ$ -space. Suppose that $G$ is the connected component of the identity of the isome…

math.GT2021★ 1 cited

Parametrized Euler class and semicohomology theory

Alessio Savini

We extend Ghys' theory about semiconjugacy to the world of measurable cocycles. More precisely, given a measurable cocycle with values into $Homeo^{+} (S^{1})$ , we can c…

math.GT2020

Entropy rigidity for foliations by strictly convex projective manifolds

Alessio Savini

Let $N$ be a compact manifold with a foliation $F_{N}$ whose leaves are compact strictly convex projective manifolds. Let $M$ be a compact manifold with a foliation $\maths…

math.GT2020

Boundary maps and reducibility for cocycles into the isometries of CAT(0)-spaces

Filippo Sarti, Alessio Savini

Let $Γ$ be a discrete countable group acting isometrically on a measurable field $X$ of CAT(0)-spaces of finite telescopic dimension over some ergodic standard Borel proba…

math.GT2020★ 6 cited

Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups

Alessio Savini

Following the work of Burger, Iozzi and Wienhard for representations, in this paper we introduce the notion of maximal measurable cocycles of a surface group. More precisely, let $…

math.GT2020★ 4 cited

Integrable tautness of isometries of complex hyperbolic spaces

Alessio Savini

Consider $n \geq 2$ . In this paper we prove that the group $PU (n, 1)$ is $1$ -taut. This result concludes the study of $1$ -tautness of rank-one Lie groups of non-compact type.…

math.GT2020★ 11 cited

Superrigidity of maximal measurable cocycles of complex hyperbolic lattices

Filippo Sarti, Alessio Savini

Let $Γ$ be a torsion-free lattice of $PU (p, 1)$ with $p \geq 2$ and let $(X, μ_{X})$ be an ergodic standard Borel probability $Γ$ -space. We prove that any maximal Zariski dense…

math.GT2019★ 4 cited

Multiplicative constants and maximal measurable cocycles in bounded cohomology

Marco Moraschini, Alessio Savini

Multiplicative constants are a fundamental tool in the study of maximal representations. In this paper we show how to extend such notion, and the associated framework, to measurabl…

math.GT2019

Equivariant maps for measurable cocycles with values into higher rank Lie groups

Alessio Savini

Let $G$ a semisimple Lie group of non-compact type and let $X_{G}$ be the Riemannian symmetric space associated to it. Suppose $X_{G}$ has dimension $n$ and it has…

math.GT2019★ 7 cited

Natural maps for measurable cocycles of compact hyperbolic manifolds

Alessio Savini

Let $G (n)$ be equal either to $PO (n, 1), PU (n, 1)$ or $PSp (n, 1)$ and let $Γ \leq G (n)$ be a uniform lattice. Denote by $H_{K}^{n}$ the hyperboli…

Similarity and superrigidity for transverse measured groupoids

Uniformly bounded representations of discrete measured groupoid into finite Von Neumann algebras

Continuous cochains on Furstenberg boundaries and injectivity of the comparison map

Projections from Furstenberg boundaries onto maximal flats and barycenter maps

Measurable bounded cohomology of t-discrete measured groupoids via resolutions

Boundaries and equivariant maps for ergodic groupoids

Kernels in measurable cohomology for transitive actions

Alternating cochains on Furstenberg boundaries and measurable cohomology

Measurable bounded cohomology of measured groupoids

Bounded Cohomology Classes of Exact Forms

Orbital cohomology and Kahler rigidity

Some explicit cocycles on the Furstenberg boundary for products of isometries of hyperbolic spaces and SL(3,K)

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

A Note on elementarity of virtual dendro-morphisms for higher rank lattices

Parametrized Kähler class and Zariski dense orbital 1-cohomology

Parametrized Euler class and semicohomology theory

Entropy rigidity for foliations by strictly convex projective manifolds

Boundary maps and reducibility for cocycles into the isometries of CAT(0)-spaces

Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups

Integrable tautness of isometries of complex hyperbolic spaces

Superrigidity of maximal measurable cocycles of complex hyperbolic lattices

Multiplicative constants and maximal measurable cocycles in bounded cohomology

Equivariant maps for measurable cocycles with values into higher rank Lie groups

Natural maps for measurable cocycles of compact hyperbolic manifolds

Measurable bounded cohomology of $t$ -discrete measured groupoids via resolutions

Some explicit cocycles on the Furstenberg boundary for products of isometries of hyperbolic spaces and $SL (3, K)$