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March 2013 On knots with icon surfaces
Mario Eudave-Muñoz
Osaka J. Math. 50(1): 271-285 (March 2013).

Abstract

An ICON surface is an incompressible compact orientable nonseparating surface properly embedded in a knot exterior. We show that for any odd positive number $n$, there exist plenty of knots whose exteriors $E$ contain an ICON surface $F$ with $\lvert \partial F\rvert =n$. We also show that our examples satisfy the $\mathbb{Z}$-conjecture, that is, $\pi_{1}(E/F)\cong \mathbb{Z}$.

Citation

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Mario Eudave-Muñoz. "On knots with icon surfaces." Osaka J. Math. 50 (1) 271 - 285, March 2013.

Information

Published: March 2013
First available in Project Euclid: 27 March 2013

zbMATH: 1348.57008
MathSciNet: MR3080640

Subjects:
Primary: 57M25

Rights: Copyright © 2013 Osaka University and Osaka City University, Departments of Mathematics

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Vol.50 • No. 1 • March 2013
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