We relate three classes of nonpositively curved metric spaces: hierarchically hyperbolic
spaces, coarsely injective spaces and strongly shortcut spaces. We show that every …

We show that Artin groups of extra-large type, and more generally Artin groups of large and
hyperbolic type, are hierarchically hyperbolic. This implies in particular that these groups …

We prove that the hierarchical hulls of finite sets of points in mapping class groups and
Teichmüller spaces are stably approximated by CAT (0) cube complexes, strengthening a …

Behrstock, Hagen, and Sisto classified 3-manifold groups admitting a hierarchically
hyperbolic space structure. However, these structures were not always equivariant with …

arXiv:2112.10681v2 [math.MG] 1 Jul 2022 Page 1 MAPPING CLASS GROUPS ARE
QUASICUBICAL HARRY PETYT Abstract. It is proved that the mapping class group of any closed …

Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity Page 1
Comment. Math. Helv. 99 (2024), 149–228 DOI 10.4171/CMH/568 © 2024 Swiss Mathematical …

This is an expository survey with two goals. 1) The primary goal is to discuss and highlight
the impact of two recent influential ideas in geometric group theory. The first of which is the …

Random walks on spaces with hyperbolic properties tend to sublinearly track geodesic rays
which point in certain hyperbolic-like directions. Qing-Rafi-Tiozzo recently introduced the …

For a closed and orientable surface of genus at least 2, we prove the surface group
extensions of the stabilizers of multicurves are hierarchically hyperbolic groups. This …

Let G be a graph of hyperbolic groups with 2-ended edge groups. We show that G is
hierarchically hyperbolic if and only if G has no distorted infinite cyclic subgroup. More …