Complex hyperbolic geometry of the figure-eight knot

Deraux, Martin; Falbel, Elisha

doi:10.2140/gt.2015.19.237

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Complex hyperbolic geometry of the figure-eight knot

Martin Deraux and Elisha Falbel

Geometry & Topology 19 (2015) 237–293

DOI: 10.2140/gt.2015.19.237

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

References

Publication

Received: 27 March 2013

Revised: 11 February 2014

Accepted: 1 May 2014

Published: 27 February 2015

Proposed: Walter Neumann

Seconded: Benson Farb, Danny Calegari

Authors

Martin Deraux
Institut Fourier Université de Grenoble 1 BP 74 Saint Martin d’Hères, Cedex France

Elisha Falbel
Institut de Mathématiques Université Pierre et Marie Curie 4 place Jussieu F-75252 Paris France

Volume 19, issue 1 (2015)