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TOROIDAL AND ANNULAR DEHN FILLINGS

Published online by Cambridge University Press:  01 May 1999

CAMERON McA. GORDON  and
YING-QING WU
CAMERON McA. GORDON
Affiliation:
Mathematical Sciences Research Institute, Berkley Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A. E-mail: [email protected]
YING-QING WU
Affiliation:
Mathematical Sciences Research Institute, Berkley Department of Mathematics, University of Iowa, Iowa City, IA 52242, U.S.A. E-mail: [email protected]
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Abstract

Suppose that $M$ is a hyperbolic 3-manifold which admits two Dehn fillings $M(r_1)$ and $M(r_2)$ such that $M(r_1)$ contains an essential annulus, and $M(r_2)$ contains an essential torus. It is known that $\Delta = \Delta (r_1, r_2) \leq 5.$ We will show that if $\Delta = 5$ then $M$ is the Whitehead sister link exterior, and if $\Delta = 4$ then $M$ is the exterior of either the Whitehead link or the 2-bridge link associated to the rational number $\frac{3}{10}$. There are infinitely many examples with $\Delta = 3$.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 78 , Issue 3 , May 1999 , pp. 662 - 700
Copyright
1999 The London Mathematical Society

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