4 papers
Periodic quasiflats in hierarchically hyperbolic spaces
Pénélope Azuelos, Mark Hagen
We prove a quasiflat closing theorem and a coarse flat torus theorem for hierarchically hyperbolic groups (HHGs). Namely, given an HHG , we prove that is hyperbolic if and o…
Uncountably many homogeneous real trees with the same valence
Pénélope Azuelos
For any cardinal , there is a unique complete real tree whose points all have valence . In this note, we show that, when , it is necessary to assume complet…
A guide to constructing free transitive actions on median spaces
Pénélope Azuelos
We construct large families of groups admitting free transitive actions on median spaces. In particular, we construct groups which act freely and transitively on the complete unive…
Perfect kernel and dynamics: from Bass-Serre theory to hyperbolic groups
Pénélope Azuelos, Damien Gaboriau
We introduce several approaches to studying the Cantor-Bendixson decomposition of and the dynamics on the (topological) space of subgroups for various families of countable groups.…