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Transactions of the American Mathematical Society

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Distance between toroidal surgeries on hyperbolic knots in the $3$-sphere


Author: Masakazu Teragaito
Journal: Trans. Amer. Math. Soc. 358 (2006), 1051-1075
MSC (2000): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9947-05-03703-7
Published electronically: April 13, 2005
Erratum: Trans. Amer. Math. Soc. 361 (2009), 3373-3374.
Correction: Trans. Amer. Math. Soc. 272 (1982), 803-807.
MathSciNet review: 2187645
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Abstract: For a hyperbolic knot in the $3$-sphere, at most finitely many Dehn surgeries yield non-hyperbolic $3$-manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed $3$-manifold containing an incompressible torus. The slope corresponding to a toroidal surgery, called a toroidal slope, is known to be integral or half-integral. We show that the distance between two integral toroidal slopes for a hyperbolic knot, except the figure-eight knot, is at most four.


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Additional Information

Masakazu Teragaito
Affiliation: Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
Email: teragai@hiroshima-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-05-03703-7
Keywords: Dehn surgery, toroidal surgery, knot
Received by editor(s): December 10, 2003
Received by editor(s) in revised form: April 7, 2004
Published electronically: April 13, 2005
Additional Notes: This work was partially supported by the Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), 14540082.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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