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Examples of 3-knots with no 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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Extract

We work throughout in the smooth category. Homomorphisms of fundamental and homology groups are induced by inclusion. An n-knot, form n ≥ 1, is an embedded n-sphere K ⊂ Sn+2. A Seifert manifold for K is a compact, connected, orientable (n + 1)-manifold V ⊂ Sn+2 with boundary ∂V = K. By [9] Seifert manifolds always exist. As in [9] let Y denote Sn+2 split along V; Y is a compact manifold with ∂Y = V0 ∪ V1, where Vt ≈ V. We say that V is a minimal Seifert manifold for K if π1Vt → π1Y is a monomorphism for t = 0, 1. (Here and throughout basepoint considerations are suppressed.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 417 - 420
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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