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math.GT2026
Coarse embeddings of products of trees as quasi-isometry invariants
Mark Hagen, Alessandro Sisto
We consider the maximal number of factors of a product of bushy trees that can be quasi-isometrically, or even coarsely embedded into various groups of interest, including mapping…
math.GT2025
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…
math.GT2024
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…