149 citations · 710 across the 38 of their papers we have counts for
4 papers · 1 filter
Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
Antoine Goldsborough, Mark Hagen, Harry Petyt +2
We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relat…
A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces
Mark Hagen, Giorgio Mangioni, Alessandro Sisto
The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying n…
Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Carolyn Abbott, Mark Hagen, Harry Petyt +1
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic gr…
Homotopy equivalent boundaries of cube complexes
Talia Fernós, David Futer, Mark Hagen
A finite-dimensional CAT(0) cube complex is equipped with several well-studied boundaries. These include the Tits boundary (which depends on the CAT(0) metric), the Roller boun…