Hyperbolic groups with logarithmic separation profile
Year: 2025
Type: article
Abstract: We prove that hyperbolic groups with logarithmic separation profiles split over cyclic groups. This shows that such groups can be inductively built from Fuchsian groups and free groups by amalgamations and HNN extensions over finite or virtually cyclic groups. However, we show that not all groups admitting such a hierarchy have logarithmic separation profile by providing an example of a surface amalgam over a cyclic group with superlogarithmic separation profile.
Source: Algebraic & Geometric Topology
Authors: Nir Lazarovich, Corentin Le Coz
Institutions: Technion – Israel Institute of Technology, Ghent University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W3208433603