Hyperbolic HHS I:Factor Systems and Quasi-convex subgroups

Abstract

In this paper we provide a procedure to obtain a non-trivial HHS structure on a hyperbolic space. In particular, we prove that given a finite collection $\mathcal{F}$ of quasi-convex subgroups of a hyperbolic group $G$, there is an HHG structure on $G$ that is compatible with $\mathcal{F}$. We will use this to provide explicit descriptions of the Gromov Boundary of hyperbolic HHS and HHG, and we recover results from Hamenstädt, Manning, Trang for the case when $G$ is hyperbolic relative to $\mathcal{F}$. Further applications in the construction of new HHG will be presented in a subsequent paper.

36 pages, 3 figures, streamlined and clarified some arguments, corrected typos. arXiv admin note: text overlap with arXiv:1604.01061 by other authors

References in corpus (1)

• Boundaries and automorphisms of hierarchically hyperbolic spaces

Cited by in corpus (2)

• On hierarchical hyperbolicity of cubical groups
• Boundaries of coned-off hyperbolic spaces