Geometric types of twisted knots
Annales mathématiques Blaise Pascal, Volume 13 (2006) no. 1, p. 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.

@article{AMBP_2006__13_1_31_0,
     author = {A\"\i t-Nouh, Mohamed and Matignon, Daniel and Motegi, Kimihiko},
     title = {Geometric types of twisted knots},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {13},
     number = {1},
     year = {2006},
     pages = {31-85},
     doi = {10.5802/ambp.213},
     mrnumber = {2233011},
     zbl = {1158.57005},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2006__13_1_31_0}
}
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/item/AMBP_2006__13_1_31_0/

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