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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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Dehn surgery on the figure 8 knot: Immersed surfaces
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by I. R. Aitchison, S. Matsumoto and J. H. Rubinstein PDF
Proc. Amer. Math. Soc. 127 (1999), 2437-2442 Request permission

Abstract:

It is known that about 70% of surgeries on the figure 8 knot give manifolds which contain immersed incompressible surfaces. We improve this to about 80% by giving a very simple proof that all even surgeries give manifolds containing such a surface. Moreover, we give a quick proof that every $(6k,t)$ surgery is virtually Haken, thereby partially dealing with some exceptional cases in Baker’s results.
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Additional Information
  • I. R. Aitchison
  • Affiliation: Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
  • Email: iain@maths.mu.oz.au
  • S. Matsumoto
  • Affiliation: Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
  • Email: saburo@is.titech.ac.jp
  • J. H. Rubinstein
  • Affiliation: Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
  • MR Author ID: 151465
  • Email: rubin@maths.mu.oz.au
  • Received by editor(s): November 12, 1996
  • Received by editor(s) in revised form: October 21, 1997
  • Published electronically: March 24, 1999
  • Additional Notes: This research was partially supported by the Australian Research Council.
  • Communicated by: Ronald A. Fintushel
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 2437-2442
  • MSC (1991): Primary 57Q35; Secondary 57M50
  • DOI: https://doi.org/10.1090/S0002-9939-99-04716-4
  • MathSciNet review: 1485454