Consider a three-dimensional cusped spherical
manifold
and suppose that the holonomy representation of
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
structure on some
Dehn surgeries of
.
The result is very similar to R. Schwartz’s spherical
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
structures on all Dehn
surgeries of slope
,
for
small enough.
