Geometric types of twisted knots
Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 31-85.

Let K be a knot in the 3-sphere S3, and Δ a disk in S3 meeting K transversely in the interior. For non-triviality we assume that |ΔK|2 over all isotopies of K in S3-Δ. Let KΔ,n(S3) be a knot obtained from K by n twistings along the disk Δ. If the original knot is unknotted in S3, we call KΔ,n a twisted knot. We describe for which pair (K,Δ) and an integer n, the twisted knot KΔ,n is a torus knot, a satellite knot or a hyperbolic knot.

DOI : 10.5802/ambp.213

Mohamed Aït-Nouh 1 ; Daniel Matignon 2 ; Kimihiko Motegi 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
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Mohamed Aït-Nouh; Daniel Matignon; Kimihiko Motegi. Geometric types of twisted knots. Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 31-85. doi : 10.5802/ambp.213. https://ambp.centre-mersenne.org/articles/10.5802/ambp.213/

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