6 papers
Constructing metric spaces from systems of walls
Harry Petyt, Abdul Zalloum, Davide Spriano
We give a general procedure for constructing metric spaces from systems of partitions. This generalises and provides analogues of Sageev's construction of dual CAT(0) cube complexe…
Largest acylindrical actions of free-by-cyclic groups
Monika Kudlinska, Harry Petyt
We show that every finitely generated free-by-cyclic group admits a largest acylindrical action on a hyperbolic space obtained by coning off maximal product subgroups of $G…
Coarse obstructions to cocompact cubulation
Zachary Munro, Harry Petyt
We provide geometric methods to give bounds on the large-scale dimension of CAT(0) cube complexes quasiisometric to a given group . In situations where these bounds conflict we…
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…
Stable cylinders and fine structures for hyperbolic groups and curve graphs
Harry Petyt, Davide Spriano, Abdul Zalloum
In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve grap…
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…