On the distance between Seifert surfaces
| dc.creator | Sakuma, Makoto | |
| dc.creator | Shackleton, Kenneth J. | |
| dc.date | 2007-01-17 | |
| dc.date | 2008-01-17 | |
| dc.date.accessioned | 2026-07-07T08:54:54Z | |
| dc.date.available | 2026-07-07T08:54:54Z | |
| dc.description | 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. | |
| dc.description | 19 pages, 1 figure. To appear in Osaka Journal of Mathematics. Minor changes including a shorter title, added references, and a research update | |
| dc.identifier | https://arxiv.org/abs/math/0701468 | |
| dc.identifier | http://arxiv.org/abs/math/0701468 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146109 | |
| dc.subject | Geometric Topology | |
| dc.subject | Combinatorics | |
| dc.subject | 57M25; 05C12 | |
| dc.title | On the distance between Seifert surfaces | |
| dc.type | text |