Zhihao Mu (CUNY)
Event Date
2026-10-21
Event Time
02:30 pm ~ 03:30 pm
Event Location
Wachman 617
Abstract: A central theme in geometric group theory is to study finitely generated groups through their large-scale geometry. Right-angled Coxeter groups (RACGs) are defined by finite graphs, and much of their large-scale geometry is visible in the combinatorics of these defining graphs. To each RACG, we can canonically associate a hyperbolic space, obtained by coning-off flats in its Davis complex. In this talk, I will characterize, in terms of combinatorics of the defining graph, when the Gromov boundary of this hyperbolic space is connected. Moreover, whenever the boundary is connected, it is also linearly connected. As an application, among one-ended RACGs, the existence of a splitting over a subgroup contained in a direct product of two infinite subgroups is preserved by quasi-isometries.