Dehn surgery and negatively curved \(3\)-manifolds (Q1807892)

This paper shows that a compact orientable 3-manifold with boundary a (possibly empty) union of tori can be obtained in only a finite number of ways (up to isometry) by performing Dehn surgeries on a hyperbolic manifold \(X\) with a collection of long slopes on tori in the boundary of \(X\).