Random Quotients of Hyperbolic Spaces with Respect to WPD Actions and Linear Connectivity of the Boundary
Year: 2026
Type: preprint
Abstract: We study random quotients of acylindrically hyperbolic groups and hierchically hyperbolic groups, whose (partial) hyperbolicity is captured by their actions on Gromov hyperbolic spaces. We show that if an acylindrically hyperbolic group $G$ acts on a Gromov hyperbolic space $X$ coarsely transitively with a WPD element, then the quotient of $X$ by the normal closure of a random element of $G$ has linearly connected boundary. If $G$ is a group with a (relative) hierarchically hyperbolic group structure, with a quasi-tree top domain $X$, then in fact the quotient of $X$ by the normal closure of a random element of $G$ has boundary homeomorphic to the Nöbeling curve.
Source: arXiv (Cornell University)
Authors: Choi, Inhyeok, Talbott, Henry
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222568003