Pénélope Azuelos

Periodic quasiflats in hierarchically hyperbolic spaces

We prove a quasiflat closing theorem and a coarse flat torus theorem for hierarchically hyperbolic groups (HHGs). Namely, given an HHG $G$, we prove that $G$ is hyperbolic if and only if it contains no $\mathbb Z^2$ subgroups and, if $A\leq G$ is virtually $\mathbb Z^n$, then there is an $A$--invariant $n$--dimensional...