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

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 |ΔK|2 over all isotopies of K in S 3 -Δ. Let K Δ,n (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.

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
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Aït-Nouh, Mohamed; Matignon, Daniel; Motegi, Kimihiko. Geometric types of twisted knots. Annales mathématiques Blaise Pascal, Volume 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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