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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Distance between toroidal surgeries on hyperbolic knots in the $3$-sphere
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by Masakazu Teragaito PDF
Trans. Amer. Math. Soc. 358 (2006), 1051-1075 Request permission

Erratum: Trans. Amer. Math. Soc. 361 (2009), 3373-3374.
Correction: Trans. Amer. Math. Soc. 272 (1982), 803-807.

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
  • MR Author ID: 264744
  • Email: teragai@hiroshima-u.ac.jp
  • 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.
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 1051-1075
  • MSC (2000): Primary 57M25
  • DOI: https://doi.org/10.1090/S0002-9947-05-03703-7
  • MathSciNet review: 2187645