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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Closed incompressible surfaces in knot complements
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by Elizabeth Finkelstein and Yoav Moriah PDF
Trans. Amer. Math. Soc. 352 (2000), 655-677 Request permission

Abstract:

In this paper we show that given a knot or link $K$ in a $2n$-plat projection with $n\ge 3$ and $m\ge 5$, where $m$ is the length of the plat, if the twist coefficients $a_{i,j}$ all satisfy $|a_{i,j}|>1$ then $S^3-N(K)$ has at least $2n-4$ nonisotopic essential meridional planar surfaces. In particular if $K$ is a knot then $S^3-N(K)$ contains closed incompressible surfaces. In this case the closed surfaces remain incompressible after all surgeries except perhaps along a ray of surgery coefficients in $\mathbb {Z}\oplus \mathbb {Z}$.
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Additional Information
  • Elizabeth Finkelstein
  • Affiliation: Department of Mathematics, (CUNY) Hunter College, New York, New York 10021
  • Email: efinkels@shiva.hunter.cuny.edu
  • Yoav Moriah
  • Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel
  • MR Author ID: 238915
  • Email: ymoriah@techunix.technion.ac.il
  • Received by editor(s): May 23, 1996
  • Received by editor(s) in revised form: October 10, 1997
  • Published electronically: September 9, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 655-677
  • MSC (1991): Primary 57M25, 57M99, 57N10
  • DOI: https://doi.org/10.1090/S0002-9947-99-02233-3
  • MathSciNet review: 1487613