Calendar

Posted September 15, 2026
Last modified October 31, 2026

Geometry and Topology Seminar Seminar website

Kushlam Srivastava, University of Wisconsin-Milwaukee
Parabolic cut pairs in boundaries of relatively hyperbolic groups

Given a relatively hyperbolic group, the topology of its Bowditch boundary is useful in understanding the underlying relatively hyperbolic structure. For example, for a connected boundary, we know from the work of Hruska–Dasgupta that the cut points are parabolic and correspond to a parabolic splitting of the group. We also know from work of Haulmark–Hruska that inseparable loxodromic cut pairs correspond to splittings over 2–ended subgroups. For some time, it was suspected that inseparable cut pairs on the boundary can only be loxodromic. However, examples of parabolic cut pairs were discovered by Hruska–Walsh. In this talk, we will present a combination theorem for relatively hyperbolic groups, which results in such parabolic cut pairs on their boundaries. We will also see that all relatively hyperbolic groups with parabolic cut pairs are characterized via this theorem.

Event contact: Pallavi Dani

Posted September 15, 2026

Geometry and Topology Seminar Seminar website

Ping Wan, University of Illinois Chicago
TBA

Event contact: Jagerynn Ting Verano