Free groups generated by two parabolic maps

Abstract

In this paper we consider a group generated by two unipotent parabolic elements of $\mathrm{SU}(2,1)$ with distinct fixed points. We give several conditions that guarantee the group is discrete and free. We also give a result on the diameter of a finite $\mathbb{R}$-circle in the Heisenberg group.

arXiv comment24 pages