On the distance between Seifert surfaces

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For a knot $K$, Kakimizu introduced a simplicial complex whose vertices are all the isotopy classes of minimal genus spanning surfaces for $K$. The first purpose of this paper is to prove the 1-skeleton of this complex has diameter bounded by a function quadratic in knot genus, whenever $K$ is atoroidal. The second purpose of this paper is to prove the intersection number of two minimal genus spanning surfaces for $K$ is also bounded by a function quadratic in knot genus, whenever $K$ is atoroidal. As one application, we prove the simple connectivity of Kakimizu's complex among all atoroidal genus 1 knots.
19 pages, 1 figure. To appear in Osaka Journal of Mathematics. Minor changes including a shorter title, added references, and a research update

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Geometric Topology, Combinatorics, 57M25; 05C12

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http://salesiana.dossiersoluciones.com/handle/123456789/146109

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701468
 http://arxiv.org/abs/math/0701468

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arXiv