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