Geometric types of twisted knots

Aït-Nouh, Mohamed; Matignon, Daniel; Motegi, Kimihiko

doi:10.5802/ambp.213

Aït-Nouh, Mohamed ¹ ; Matignon, Daniel ² ; Motegi, Kimihiko ³

¹ Department of Mathematics University of California at Santa Barbara Boston, MA 02215 USA
² CMI, UMR 6632 du CNRS Université d’Aix-Marseille I 39, rue Joliot Curie F-13453 Marseille Cedex 13 FRANCE
³ Department of Mathematics Nihon University Tokyo 156-8550 JAPAN

Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 31-85.

Résumé

Let $K$ be a knot in the $3$ -sphere $S^{3}$ , and $Δ$ a disk in $S^{3}$ meeting $K$ transversely in the interior. For non-triviality we assume that $| Δ \cap K | \geq 2$ over all isotopies of $K$ in $S^{3} - \partial Δ$ . Let $K_{Δ, n}$ ( $\subset S^{3}$ ) be a knot obtained from $K$ by $n$ twistings along the disk $Δ$ . If the original knot is unknotted in $S^{3}$ , we call $K_{Δ, n}$ a twisted knot. We describe for which pair $(K, Δ)$ and an integer $n$ , the twisted knot $K_{Δ, n}$ is a torus knot, a satellite knot or a hyperbolic knot.

MR Zbl

DOI : 10.5802/ambp.213

Affiliations des auteurs :

Aït-Nouh, Mohamed ¹ ; Matignon, Daniel ² ; Motegi, Kimihiko ³

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Aït-Nouh, Mohamed; Matignon, Daniel; Motegi, Kimihiko. Geometric types of twisted knots. Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 31-85. doi : 10.5802/ambp.213. http://www.numdam.org/articles/10.5802/ambp.213/

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