SPHERICAL CR DEHN SURGERIES

Consider a three-dimensional cusped spherical CR manifold M and suppose that the holonomy representation of pi(1)(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 is an element of Q(+) small enough.