Geometric types of twisted knots

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

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

Annales mathématiques Blaise Pascal, Tome 13 (2006), p. 31-85 / Harvested from Numdam

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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.

Publié le : 2006-01-01

MR 2233011 | Zbl 1158.57005

DOI : https://doi.org/10.5802/ambp.213

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

Aït-Nouh, Mohamed; Matignon, Daniel; Motegi, Kimihiko. Geometric types of twisted knots. Annales mathématiques Blaise Pascal, Tome 13 (2006) pp. 31-85. doi : 10.5802/ambp.213. http://gdmltest.u-ga.fr/item/AMBP_2006__13_1_31_0/

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