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A Note on Finite Dehn Fillings

Open Access article
 Printed: Jun 1999
  • S. Boyer
  • X. Zhang
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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 the minimal 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 yield manifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most $3$.
MSC Classifications: 57M25, 57R65 show english descriptions Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Surgery and handlebodies
57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45}
57R65 - Surgery and handlebodies

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