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math.GR2023
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…
math.GT2023
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…