In this survey article, we present some panorama of groups acting on metric spaces of non-
positive curvature. We introduce the main examples and their rigidity properties, we show …

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 …

PROPER CAT(0) ACTIONS OF UNIPOTENT-FREE LINEAR GROUPS Page 1 J. Inst. Math.
Jussieu (2025), 1–15 doi:10.1017/S147474802400046X 1 PROPER CAT(0) ACTIONS OF …

This is a survey of topological properties of open, complete nonpositively curved manifolds
which may have infinite volume. Topics include topology of ends, restrictions on the …

Button observed that finitely generated matrix groups containing no nontrivial unipotent
matrices behave much like groups admitting proper actions by semisimple isometries on …

We study representations G→ H where G is either a simple Lie group with real rank at least
2 or an infinite dimensional orthogonal group of some quadratic form of finite index at least 2 …

We prove that there exists no irreducible representation of the identity component of the
isometry group PO (1, n) PO (1, n) of the real hyperbolic space of dimension n into the group …

We study algebraic conditions on a group under which every properly discontinuous,
isometric-action on a Hadamard manifold has a-invariant Busemann function, and for such …

Let $\Gamma $ be a finitely generated group of matrices over $\mathbb {C} $. We construct
an isometric action of $\Gamma $ on a complete CAT (0) space $ X $ such that the …

We study representations $ G\to H $ where $ G $ is either a simple Lie group with real rank
at least 2 or an infinite dimensional orthogonal group of some quadratic form of finite index …