Year: 2026
Type: article
Abstract: Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. In this paper, a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is shown to be closed under quasi‐isometry. Additionally, these groups share some of the properties of limit groups. In particular, groups quasi‐isometric to limit groups are shown to be locally extended residually finite (LERF) and virtually toral relatively hyperbolic.
DOI: 10.1112/jlms.70698
Author: Aaron W. Messerla
Institution: University of Illinois Chicago
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4320560352