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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Toroidal surgeries on hyperbolic knots
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by Masakazu Teragaito PDF
Proc. Amer. Math. Soc. 130 (2002), 2803-2808 Request permission

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
  • MR Author ID: 264744
  • Email: teragai@hiroshima-u.ac.jp
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2803-2808
  • MSC (2000): Primary 57M50
  • DOI: https://doi.org/10.1090/S0002-9939-02-06420-1
  • MathSciNet review: 1900888