Vol. 284, No. 2, 2016

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Spherical CR Dehn surgeries

Miguel Acosta

Vol. 284 (2016), No. 2, 257–282

Consider a three-dimensional cusped spherical CR manifold M and suppose that the holonomy representation of π1(M) can be deformed in such a way that the peripheral holonomy is generated by a nonparabolic element. We prove that, in this case, there is a spherical CR structure on some Dehn surgeries of M. The result is very similar to R. Schwartz’s spherical CR Dehn surgery theorem, but has weaker hypotheses and does not give the uniformizability of the structure. We apply our theorem in the case of the Deraux–Falbel structure on the figure eight knot complement and obtain spherical CR structures on all Dehn surgeries of slope 3 + r, for r + small enough.

spherical CR, Dehn surgery, $(G,X)$-structures, figure-eight knot
Mathematical Subject Classification 2010
Primary: 32V05, 57M25, 57M50
Received: 14 September 2015
Revised: 21 January 2016
Accepted: 26 January 2016
Published: 30 August 2016
Miguel Acosta
Université Pierre et Marie Curie
4 Place Jussieu
75252 Paris CEDEX 05