## Journal of Differential Geometry

### A Proof of the Finite Filling Conjecture

#### Abstract

Let M be a compact, connected, orientable, hyperbolic 3-manifold whose boundary is a torus. We show that there are at most five slopes on $\partial M$ whose associated Dehn fillings have either a finite or an infinite cyclic fundamental group. Furthermore, the distance between two slopes yielding such manifolds is no more than three, and there is at most one pair of slopes which realize the distance three. Each of these bounds is realized when M is taken to be the exterior of the figure-8 sister knot.

#### Article information

Source
J. Differential Geom., Volume 59, Number 1 (2001), 87-176.

Dates
First available in Project Euclid: 20 July 2004

https://projecteuclid.org/euclid.jdg/1090349281

Digital Object Identifier
doi:10.4310/jdg/1090349281

Mathematical Reviews number (MathSciNet)
MR1909249

Zentralblatt MATH identifier
1030.57024

#### Citation

Boyer, Steven; Zhang, Xingru. A Proof of the Finite Filling Conjecture. J. Differential Geom. 59 (2001), no. 1, 87--176. doi:10.4310/jdg/1090349281. https://projecteuclid.org/euclid.jdg/1090349281