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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Closed incompressible surfaces
in knot complements


Authors: Elizabeth Finkelstein and Yoav Moriah
Journal: Trans. Amer. Math. Soc. 352 (2000), 655-677
MSC (1991): Primary 57M25, 57M99, 57N10
Published electronically: September 9, 1999
MathSciNet review: 1487613
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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
Email: ymoriah@techunix.technion.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02233-3
PII: S 0002-9947(99)02233-3
Received by editor(s): May 23, 1996
Received by editor(s) in revised form: October 10, 1997
Published electronically: September 9, 1999
Article copyright: © Copyright 1999 American Mathematical Society