Abstract

Let M \mathcal {M} be a 1 1 -cusped hyperbolic 3 3 -manifold whose cusp shape is quadratic. We show that there exists c = c ( M ) c=c(\mathcal {M}) such that the number of hyperbolic Dehn fillings of M \mathcal {M} with any given volume v v is uniformly bounded by c c .

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