On spherical CR uniformization of 3-manifolds

2014/10/02 by Martin Deraux, Deraux, Martin · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Point processes and geometric inequalities

paper · doi:10.48550/arxiv.1410.0659

openalex publication_date 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the discrete representations of 3-manifold groups into PU(2,1) that appear in the Falbel-Koseleff-Rouillier census, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjugate images, even though they represent different 3-manifold groups. This illustrates the fact that a discrete representation π₁(M)→ PU(2,1) with cyclic unipotent boundary holonomy is not in general the holonomy of a spherical CR uniformization of M.

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• SL(n,C)- Representation spaces of Knot Groups

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