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A Note on Finite Dehn Fillings

Published online by Cambridge University Press:  20 November 2018

S. Boyer  and
X. Zhang
S. Boyer
Affiliation:
Département de mathématiques UQAM P.O. Box 8888, Station A Montréal, Québec H3C 3P8, email: boyer@math.uqam.ca
X. Zhang
Affiliation:
Department of Mathematics Oklahoma State University Stillwater, Oklahoma 74078-0001 USA, email: xingru@math.okstate.edu
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Abstract

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Let $M$ be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if theminimal Culler-Shalen norm of a non-zero class in ${{H}_{1}}(\partial M)$ is larger than 8, then the finite surgery conjecture holds for $M$. This means that there are at most 5 Dehn fillings of $M$ which can yieldmanifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.

Keywords

57M2557R65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 2 , 01 June 1999 , pp. 149 - 154
Copyright
Copyright © Canadian Mathematical Society 1999

References

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