## 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 $\mathbb {Z}\oplus \mathbb {Z}$.## References

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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