23 citations · 88 across the 14 of their papers we have counts for
17 papers
The real spectrum compactification of character varieties
Marc Burger, Alessandra Iozzi, Anne Parreau +1
We study the real spectrum compactification of character varieties of finitely generated groups in semisimple Lie groups. This provides a compactification with good topological pro…
On projective Anosov subgroups of symplectic groups
Maria Beatrice Pozzetti, Konstantinos Tsouvalas
We prove that a word hyperbolic group whose Gromov boundary properly contains a -sphere cannot admit a projective Anosov representation into , $m\i…
Weyl chamber length compactification of the maximal character variety
Marc Burger, Alessandra Iozzi, Anne Parreau +1
We study the vectorial length compactification of the space of conjugacy classes of maximal representations of the fundamental group of a closed hyperbolic surface in ${\rm…
Positive crossratios, barycenters, trees and applications to maximal representations
Marc Burger, Alessandra Iozzi, Anne Parreau +1
We study metric properties of maximal framed representations of fundamental groups of surfaces in symplectic groups over real closed fields, interpreted as actions on Bruhat-Tits b…
Geometric limits of cyclic subgroups of SO_0(1, k+1) and SU(1, k+1)
Sara Maloni, Maria Beatrice Pozzetti
We study geometric limits of convex-cocompact cyclic subgroups of the rank 1 groups SO_0(1, k+1) and SU(1, k+1). We construct examples of sequences of subgroups of such groups G th…
The real spectrum compactification of character varieties: characterizations and applications
Marc Burger, Alessandra Iozzi, Anne Parreau +1
We announce results on a compactification of general character varieties that has good topological properties and give various interpretations of its ideal points. We relate this t…
Conformality for a robust class of non-conformal attractors
Beatrice Pozzetti, Andrés Sambarino, Anna Wienhard
In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and…
Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
Bruno Duchesne, Jean Lécureux, Maria Beatrice Pozzetti
We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite dimensional Hermitian symmetric spaces, which allows us to define maximal repres…
A structure theorem for geodesic currents and length spectrum compactifications
Marc Burger, Alessandra Iozzi, Anne Parreau +1
We find a canonical decomposition of a geodesic current on a surface of finite type arising from a topological decomposition of the surface along special geodesics. We show that ea…
The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups
Federico Franceschini, Roberto Frigerio, Maria Beatrice Pozzetti +1
We construct combinatorial volume forms of hyperbolic three manifolds fibering over the circle. These forms define non-trivial classes in bounded cohomology. After introducing a ne…
Basmajian-type inequalities for maximal representations
Federica Fanoni, Maria Beatrice Pozzetti
For suitable metrics on the locally symmetric space associated to a maximal representation, we prove inequalities between the length of the boundary and the lengths of orthogeodesi…
Maximal representations, non Archimedean Siegel spaces, and buildings
Marc Burger, Maria Beatrice Pozzetti
Let be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in …
Classification of tight homomorphisms
Oskar Hamlet, Maria Beatrice Pozzetti
A totally geodesic map between Hermitian symmetric spaces is tight if its image contains geodesic triangles of maximal area. Tight maps were first i…
Maximal representations of complex hyperbolic lattices in SU(m,n)
Maria Beatrice Pozzetti
Let denote a lattice in , with greater than 1. We show that there exists no Zariski dense maximal representation with target if . The proof is geo…
Extending higher dimensional quasi-cocycles
R. Frigerio, M. B. Pozzetti, A. Sisto
Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group…
Isometric Embeddings in Bounded Cohomology
Michelle Bucher, Marc Burger, Roberto Frigerio +3
This paper is devoted to the construction of norm-preserving maps between bounded cohomology groups. For a graph of groups with amenable edge groups we construct an isometric embed…
Isometric properties of relative bounded cohomology
Michelle Bucher, Marc Burger, Roberto Frigerio +3
We show that the isomorphism induced by the inclusion of pairs between the relative bounded cohomology of and the bounded cohomology of is…