5 papers · 1 filter
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…
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…
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…