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On primitive/Seifert-fibered constructions

Published online by Cambridge University Press:  26 April 2005

KATURA MIYAZAKI  and
KIMIHIKO MOTEGI
KATURA MIYAZAKI
Affiliation:
Faculty of Engineering, Tokyo Denki University, 2-2 Kanda-Nishikicho, Tokyo 101-8457, Japan. e-mail: miyazaki@cck.dendai.ac.jp
KIMIHIKO MOTEGI
Affiliation:
Department of Mathematics, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan. e-mail: motegi@math.chs.nihon-u.ac.jp
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Abstract

J. Dean introduced the notion of primitive/Seifert-fibered knots and constructions to explain how Dehn surgeries on knots produce small Seifert fibered manifolds. We determine non-hyperbolic, primitive/Seifert-fibered knots, and show that for such knots any integral, small Seifert fibered surgery arises from a primitive/Seifert-fibered construction. We also show that any 2-orbifold $S^2(n_1, n_2, n_3)$ with a pair of indices coprime becomes the base orbifold of a Seifert fibered manifold obtained by Dehn surgery on a hyperbolic, primitive/Seifert-fibered knot in $S^3$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 3 , May 2005 , pp. 421 - 435
Copyright
2005 Cambridge Philosophical Society

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