5 citations · 5 across the 10 of their papers we have counts for
11 papers
CAT(0) square complexes that do not embed into finite products of trees
James Davies, Harry Petyt
Answering a question of Chepoi and Hagen, we give two constructions of bounded degree CAT(0) square complexes that cannot be isometrically embedded into any finite product of trees…
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…
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…
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…
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…
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…
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…
Hyperbolic models for CAT(0) spaces
Harry Petyt, Davide Spriano, Abdul Zalloum
We introduce two new tools for studying CAT(0) spaces: \emph{curtains}, versions of cubical hyperplanes; and the \emph{curtain model}, a counterpart of the curve graph. These tools…
Projection complexes and quasimedian maps
Mark Hagen, Harry Petyt
We use the projection complex machinery of Bestvina--Bromberg--Fujiwara to study hierarchically hyperbolic groups. In particular, we show that if the group has a BBF colouring and…
Unbounded domains in hierarchically hyperbolic groups
Harry Petyt, Davide Spriano
We investigate unbounded domains in hierarchically hyperbolic groups and obtain constraints on the possible hierarchical structures. Using these insights, we characterise the struc…
Hierarchically hyperbolic groups and uniform exponential growth
Carolyn Abbott, Thomas Ng, Davide Spriano +2
We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For example, any hierarchically hype…