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On the existence of minimal Seifert manifolds

Published online by Cambridge University Press:  24 October 2008

Daniel S. Silver
Daniel S. Silver
Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, U.S.A.
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Abstract

For n ≥ 3, an n-knot K has a minimal Seifert manifold if and only if its group is isomorphic to an HNN-extension with finitely presented base. In this case, any Seifert manifold for K can be converted to a minimal Seifert manifold for K by some finite sequence of ambient 0- and 1-surgeries.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 103 - 109
Copyright
Copyright © Cambridge Philosophical Society 1993

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