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Spherical CR uniformization of Dehn surgeries of the Whitehead link complement

Miguel Acosta

Geometry & Topology 23 (2019) 2593–2664

We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as a starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the complex hyperbolic plane 2. We deform the Ford domain of Parker and Will in 2 in a one-parameter family. On one side, we obtain infinitely many spherical CR uniformizations on a particular Dehn surgery on one of the cusps of the Whitehead link complement. On the other side, we obtain spherical CR uniformizations for infinitely many Dehn surgeries on the same cusp of the Whitehead link complement. These manifolds are parametrized by an integer n 4, and the spherical CR structure obtained for n = 4 is the Deraux–Falbel spherical CR uniformization of the figure eight knot complement.

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spherical CR geometry, complex hyperbolic geometry, Dehn surgery, uniformization, Whitehead link, Ford domain
Mathematical Subject Classification 2010
Primary: 51M10, 57M50
Secondary: 22E40, 32V05
Received: 22 March 2018
Revised: 6 November 2018
Accepted: 5 February 2019
Published: 13 October 2019
Proposed: Walter Neumann
Seconded: Benson Farb, Jean-Pierre Otal
Miguel Acosta
Unité de recherche en Mathématiques
Université du Luxembourg
Campus Belval