Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy

2023/02/10 by Messerla, Aaron W.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2302.05344

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 LERF and virtually toral relatively hyperbolic.

Related

• Relatively hyperbolic groups with fixed peripherals
• Relatively hyperbolic groups: geometry and quasi-isometric invariance
• Quasi-isometry rigidity of groups
• Quasi-Isometries, Boundaries and JSJ-Decompositions of Relatively\n Hyperbolic Groups
• Property (QT) of relatively hierarchically hyperbolic groups