Mathematical Proceedings of the Cambridge Philosophical Society

On primitive/Seifert-fibered constructions

a1 Faculty of Engineering, Tokyo Denki University, 2-2 Kanda-Nishikicho, Tokyo 101-8457, Japan. e-mail:
a2 Department of Mathematics, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan. e-mail:

Article author query
miyazaki k   [Google Scholar] 
motegi k   [Google Scholar] 


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 $S^3$.

(Published Online April 26 2005)
(Received September 12 2003)
(Revised January 26 2004)


1 Supported in part by Grant-in-Aid for Scientific Research (No. 10640091), Ministry of Education, Science, Sports and Culture.

2 Supported in part by Grant-in-Aid for Encouragement of Young Scientists (No. 11740051), Ministry of Education, Science, Sports and Culture.