On the distance between two Seifert surfaces of a knot
Sakuma, Makoto ; Shackleton, Kenneth J.
Osaka J. Math., Tome 46 (2009) no. 1, p. 203-221 / Harvested from Project Euclid
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For a knot $K$ in $\mathbb{S}^{3}$, 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.
Publié le : 2009-03-15
Classification:  57M25,  05C12 
@article{1235574044,
     author = {Sakuma, Makoto and Shackleton, Kenneth J.},
     title = {On the distance between two Seifert surfaces of a knot},
     journal = {Osaka J. Math.},
     volume = {46},
     number = {1},
     year = {2009},
     pages = { 203-221},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1235574044}
}

Sakuma, Makoto; Shackleton, Kenneth J. On the distance between two Seifert surfaces of a knot. Osaka J. Math., Tome 46 (2009) no. 1, pp.  203-221. http://gdmltest.u-ga.fr/item/1235574044/