arXiv subjects

Aaron W. Messerla

Publications and source records attributed to Aaron W. Messerla.

2 recordsLinked to original sources

arXiv2023

On the Bowditch boundary of a free group with random cyclic peripheral groups

The topology of the Bowditch boundary of a relatively hyperbolic group pair gives information about relative splittings of the group. It is therefore interesting to ask if there is generic behavior of this boundary. The purpose of this article is to show that in the case of a non-abelian free group with cyclic peripheral structure, there is not a generic case. This goal is accomplished by showing the minimal size of cut sets in the boundary increases as the lengths of the random words generating the peripheral structure go to infinity.

math.GR↗

arXiv2023

Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy

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.

math.GR↗