Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T14:10:26.439Z Has data issue: false hasContentIssue false

A note concerning Seifert manifolds for 2-knots

Published online by Cambridge University Press:  24 October 2008

Bruce Trace
Affiliation:
Department of Mathematics, University of Alabama, University, AL 35486

Abstract

Elementary observations yield new classes of knotted 2-spheres in S4 which do not admit Punct (# S1 × S2) as a Seifert manifold. This provides a rather painless proof which re-establishes the existence of non-ribbon 2-knots.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Cochran, T.. Ribbon knots in S 4. J. London Math. Soc. (2) 28 (1983), 563576.Google Scholar
[2]Hempel, J.. 3-Manifolds, Annals of Math. Studies, vol. 86 (Princeton University Press, 1976).Google Scholar
[3]Hitt, L. R.. Examples of higher-dimensional slice knots which are not ribbon knots. Proc. Amer. Math. Soc. 77 (1979), 291297.Google Scholar
[4]Rolfsen, D., Knots and Links (Publish or Perish, 1976).Google Scholar
[5]Ruberman, D.. Doubly slice knots and the Casson-Gordon invariants. Trans. Amer. Math. Soc. 279 (1983), 569588.Google Scholar
[6]Trace, B.. Some comments concerning Levine's approach to slicing classical knots (To appear).Google Scholar
[7]Trace, B.. A note concerning the 3-manifolds which span certain surfaces in the 4-ball (To appear).Google Scholar
[8]Yanagawa, T.. On ribbon 2-knots – the 3-manifold bounded by the 2-knots. Osaka J. Math. 6 (1969), 447464.Google Scholar