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- Mohamed Aït-Nouh, D. Matignon, Kimihiko Motegi
- 2006

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)

Let K be a knot in the 3-sphere S3, and D a disc in S3 meeting K transversely more than once in the interior. For non-triviality we assume that |K ∩D| ≥ 2 over all isotopy of K. Let Kn(⊂ S3) be a knot obtained from K by cutting and n-twisting along the disc D (or equivalently, performing 1/n-Dehn surgery on ∂D). Then we prove the following: (1) IfK is a… (More)

- MASAKAZU TERAGAITO, Ronald A. Fintushel, Takeshi Kaneto, Kimihiko Motegi, Hiroshi Goda, Makoto Ozawa
- 2002

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 K be a knot in the 3-sphere S3 and D a disk in S3 meeting K transversely more than once in the interior. For nontriviality we assume that |D ∩K| 2 over all isotopies of K in S3 − ∂D. Let KD,n (⊂ S3) be a knot obtained from K by n twisting along the disk D. We prove that if K is a trivial knot and KD,n is a graph knot, then |n| 1 or K and D form a… (More)

- H Ueda, Shogo Asano, Masanao Abe, Kimihiko Motegi
- Naika. Internal medicine
- 1964

- Kimihiko Motegi
- Naika. Internal medicine
- 1965

- Kimihiko Motegi, Hyun-Jong Song
- 2005

Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic knots in the 3-sphere S? It is conjectured that if r -surgery on a hyperbolic knot in S yields a Seifert fiber space, then r is an integer. We show that for each integer n ∈ Z, there exists a tunnel number one, hyperbolic knot Kn in S 3 such that n-surgery on Kn produces a small… (More)

- Kimihiko Motegi
- 2010

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)

A 3-manifold is toroidal if it contains an essential torus, i.e., an incompressible torus not parallel to a boundary component. A knot K in S3 is called a periodic knot with period p if there is a homeomorphism f : S3 → S3 such that f(K) = K, Fix(f)∩K = ∅, and Fix(f) is a circle. We call f a periodic map of K. For a knot K in a 3-manifold M ⊂ S3 we denote… (More)