Complex hyperbolic geometry of the figure eight knot

Abstract

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.

References in corpus (3)

• Tetrahedra of flags, volume and homology of SL(3)
• Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity
• Branched Spherical CR structures on the complement of the figure eight knot

Cited by in corpus (16)

• A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
• A complex hyperbolic Riley slice
• Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity
• Deformation of hyperbolic manifolds in $\mathrm{PGL}(n,\mathbf{C})$ and discreteness of the peripheral representations
• Spherical CR uniformization of Dehn surgeries of the Whitehead link complement
• Character varieties for real forms
• Hybrid lattices and thin subgroups of Picard modular groups
• Spherical CR Dehn Surgery
• A uniformizable spherical CR structure on a two-cusped hyperbolic 3-manifold
• Slim curves, limit sets and spherical CR uniformisations
• On the limit set of a spherical CR uniformization
• A construction of representations of 3-manifold groups into PU(2,1) through Lefschetz fibrations
• Spherical CR uniformization of the magic 3-manifold
• $\mathrm{SL}(3,\mathbb{C})$-character varieties of two-generator groups
• Redundancy of triangle groups in spherical CR representations
• Flag structures on real 3-manifolds