Discrete two-generator subgroups of PSL(2,Q_p)

Abstract: Due to work of Gilman, Rosenberger, Purzitsky and many others, discrete two-generator subgroups of PSL(2,R) have been completely classified by studying their action by Möbius transformations on the hyperbolic plane. Here we aim to classify discrete two-generator subgroups of PSL(2,Q_p) by studying their action by isometries on the Bruhat-Tits tree. We first give a general structure theorem for two-generator groups acting by isometries on a tree, which relies on certain Klein-Maskit combination theorems. We will then discuss how this theorem can be applied to determine discreteness of a two-generator subgroup of PSL(2,Q_p). This is ongoing work in collaboration with Jeroen Schillewaert.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle