Complex hyperbolic geometry of the figure eight knot

Martin Deraux (1) , Elisha Falbel (2, 3)

1 IF - Institut Fourier
2 IMJ - Institut de Mathématiques de Jussieu
3 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs

We show that the figure eight knot complement admits a uniformizable spherical CR structure, i.e. it occurs as the manifold at infinity of a complex hyperbolic orbifold. The uniformization is unique provided we require the peripheral subgroups to have unipotent holonomy.

Domaines: Topologie géométrique [math.GT]

Martin Deraux, Elisha Falbel. Complex hyperbolic geometry of the figure eight knot. Geometry and Topology, 2015, 19, pp.237-293. ⟨10.2140/gt.2015.19.237⟩. ⟨hal-00805427v2⟩