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Redundancy of triangle groups in spherical CR representations

Abstract : Falbel, Koseleff and Rouillier computed a large number of boundary unipotent CR representations of fundamental groups of non compact three-manifolds. Those representations are not always discrete. By experimentally computing their limit set, one can determine that those with fractal limit sets are discrete. Many of those discrete representations can be related to (3,3,n) complex hyperbolic triangle groups. By exact computations, we verify the existence of those triangle representations, which have boundary unipotent holonomy. We also show that many representations are redundant: for n fixed, all the (3,3,n) representations encountered are conjugate and only one among them is uniformizable.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02867990
Contributor : Raphaël Alexandre Connect in order to contact the contributor
Submitted on : Thursday, October 28, 2021 - 11:58:50 AM
Last modification on : Tuesday, November 16, 2021 - 4:03:03 AM

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Raphaël Alexandre. Redundancy of triangle groups in spherical CR representations. 2021. ⟨hal-02867990v2⟩

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