Free groups generated by two parabolic maps

Published 4 Feb 2022 in math.GT | (2202.02244v2)

Abstract: In this paper we consider a group generated by two unipotent parabolic elements of ${\rm SU}(2,1)$ 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.

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