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Toroidal surgeries on hyperbolic knots

Author: Masakazu Teragaito
Journal: Proc. Amer. Math. Soc. 130 (2002), 2803-2808
MSC (2000): Primary 57M50
Published electronically: February 4, 2002
MathSciNet review: 1900888
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Abstract: For a hyperbolic knot $K$ in $S^3$, a toroidal surgery is Dehn surgery which yields a $3$-manifold containing an incompressible torus. It is known that a toroidal surgery on $K$ is an integer or a half-integer. In this paper, we prove that all integers occur among the toroidal slopes of hyperbolic knots with bridge index at most three and tunnel number one.

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Additional Information

Masakazu Teragaito
Affiliation: Department of Mathematics and Mathematics Education, Faculty of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima 739-8524, Japan

Received by editor(s): December 6, 2000
Received by editor(s) in revised form: April 18, 2001
Published electronically: February 4, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society