Volume 19, issue 1 (2015)

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Complex hyperbolic geometry of the figure-eight knot

Martin Deraux and Elisha Falbel

Geometry & Topology 19 (2015) 237–293
Abstract

We show that the figure-eight knot complement admits a uniformizable spherical $CR$ structure, ie 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.

Keywords
spherical CR structures, geometric structures on $3$–manifolds, complex hyperbolic geometry
Mathematical Subject Classification 2010
Primary: 32V05, 57M50
Secondary: 22E40