Redundancy of hyperbolic triangle groups in spherical CR representations

Raphaël V Alexandre (1, 2, 3)

1 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 SU - Sorbonne Université

Falbel, Koseleff and Rouillier computed a large number of boundary unipotent CR representations. Those representations are not always discrete. By experimentally computing their limit set, one can determine that those with fractal limit sets are discrete. Most of those discrete representations can be classified into (3, 3, n) complex hyperbolic triangle groups. By exact computations, we verify the existence of those triangle representations, which have unipotent boundary holonomy. We also show that many representations are redundant: for n fixed, all the (3, 3, n) representations encountered are conjugated and only one among them is uniformizable.

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Raphaël V Alexandre. Redundancy of hyperbolic triangle groups in spherical CR representations. 2020. ⟨hal-02867990v1⟩