Kimihiko Motegi

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Let K be a knot in the 3-sphere S, and ∆ a disk in S meeting K transversely in the interior. For non-triviality we assume that |∆ ∩K| ≥ 2 over all isotopies of K in S − ∂∆. Let K∆,n(⊂ S) be a knot obtained from K by n twistings along the disk ∆. If the original knot is unknotted in S, we call K∆,n a twisted knot. We describe for which pair (K,∆) and an(More)
For a hyperbolic knot K in S3, a toroidal surgery is Dehn surgery which yields a 3-manifold containing an incompressible torus. It is known that a toroidal surgery on K is an integer or a half-integer. In this paper, we prove that all integers occur among the toroidal slopes of hyperbolic knots with bridge index at most three and tunnel number one.
We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean’s primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert-fibered surgeries arise from Dean’s primitive/Seifert-fibered construction. The (−3, 3, 5)-pretzel knot belongs to both of the infinite(More)
Let V be a standardly embedded solid torus in S3 with a meridianpreferred longitude pair {p., X) and K a knot contained in V . We assume that K is unknotted in S3 . Let fn be an orientation-preserving homeomorphism of V which sends X to X + np. Then we get a twisted knot K„ = f„ {K) in SK Primeness of twisted knots is discussed and we prove : A twisted knot(More)