On the number of hyperbolic Dehn fillings of a given volume

Jeon, BoGwang

doi:10.1090/tran/8371

On the number of hyperbolic Dehn fillings of a given volume
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Trans. Amer. Math. Soc. 374 (2021), 3947-3969 Request permission

Abstract:

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

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