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arXiv · 2302.05344

Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy

Aaron W. Messerla
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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.

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Aaron W. Messerla. 2023-02-10. Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy. https://arxiv.org/abs/2302.05344

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