149 citations · 595 across the 59 of their papers we have counts for
8 papers · 1 filter
Acylindrical actions on projection complexes
Mladen Bestvina, Ken Bromberg, Koji Fujiwara +1
We simplify the construction of projection complexes due to Bestvina-Bromberg-Fujiwara. To do so, we introduce a sharper version of the Behrstock inequality, and show that it can a…
What is a hierarchically hyperbolic space?
Alessandro Sisto
The first part of this survey is a heuristic, non-technical discussion of what an HHS is, and the aim is to provide a good mental picture both to those actively doing research on H…
Gromov's random monsters do not act non-elementarily on hyperbolic spaces
Dominik Gruber, Alessandro Sisto, Romain Tessera
We show that Gromov's monster groups arising from i.i.d. labelings of expander graphs do not admit non-elementary actions on geodesic hyperbolic spaces. The proof relies on compari…
Quasiflats in hierarchically hyperbolic spaces
Jason Behrstock, Mark F Hagen, Alessandro Sisto
The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the…
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…
Groups with no coarse embeddings into hyperbolic groups
David Hume, Alessandro Sisto
We introduce an obstruction to the existence of a coarse embedding of a given group or space into a hyperbolic group, or more generally into a hyperbolic graph of bounded degree. T…