On spherical CR uniformization of 3-manifolds

Martin Deraux (1)

1 IF - Institut Fourier

We consider the three discrete representations in the Falbel-Koseleff-Rouillier census where the peripheral subgroups have cyclic 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 $\pi_1(M)\rightarrow PU(2,1)$ with cyclic unipotent boundary holonomy is not in general the holonomy of a spherical CR uniformization of $M$.

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

Martin Deraux. On spherical CR uniformization of 3-manifolds. Experimental Mathematics, 2015, 24 (3), pp 355-370. ⟨10.1080/10586458.2014.996835⟩. ⟨hal-01070158⟩