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

DOI:
https://doi.org/10.1090/S0002-9947-99-02233-3

Published electronically:
September 9, 1999

MathSciNet review:
1487613

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that given a knot or link in a -plat projection with and , where is the length of the plat, if the twist coefficients all satisfy then has at least nonisotopic essential meridional planar surfaces. In particular if is a knot then contains closed incompressible surfaces. In this case the closed surfaces remain incompressible after all surgeries except perhaps along a ray of surgery coefficients in .

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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:
https://doi.org/10.1090/S0002-9947-99-02233-3

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