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Geometric types of twisted knots

Mohamed Aït-NouhDaniel MatignonKimihiko Motegi — 2006

Annales mathématiques Blaise Pascal

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 K | 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 . 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.

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