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September, 2001 A Proof of the Finite Filling Conjecture
Steven Boyer, Xingru Zhang
J. Differential Geom. 59(1): 87-176 (September, 2001). DOI: 10.4310/jdg/1090349281

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.

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Steven Boyer. Xingru Zhang. "A Proof of the Finite Filling Conjecture." J. Differential Geom. 59 (1) 87 - 176, September, 2001. https://doi.org/10.4310/jdg/1090349281

Information

Published: September, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1030.57024
MathSciNet: MR1909249
Digital Object Identifier: 10.4310/jdg/1090349281

Rights: Copyright © 2001 Lehigh University

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Vol.59 • No. 1 • September, 2001
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