In the context of CAT (0) cubical groups, we develop an analogue of the theory of curve
complexes and subsurface projections. The role of the subsurfaces is played by a collection …

A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general
construction of many actions of groups on quasi-trees. The groups we can handle include …

Hierarchically hyperbolic spaces provide a common framework for studying mapping class
groups of finite-type surfaces, Teichmüller space, right-angled Artin groups, and many other …

The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in
a standard product region. For hierarchically hyperbolic groups, this coincides with the …

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 …

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 …

We build an analogue of the Gromov boundary for any proper geodesic metric space, hence
for any finitely generated group. More precisely, for any proper geodesic metric space $ X …

Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified
framework for studying the mapping class group, right-angled Artin and Coxeter groups, and …

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 …

We study the coarse geometry of the mapping class group of a compact orientable surface.
We show that, apart from a few low-complexity cases, any quasi-isometric embedding of a …