New examples of non–slice, algebraically slice knots
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- by Charles Livingston PDF
- Proc. Amer. Math. Soc. 130 (2002), 1551-1555 Request permission
Abstract:
For $n >1$, if the Seifert form of a knotted $2n-1$–sphere $K$ in $S^{2n+ 1}$ has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three. However, in the three–dimensional case it is true that if the metabolizer has a basis represented by a strongly slice link, then $K$ is slice. The question has been asked as to whether it is sufficient that each basis element is represented by a slice knot to assure that $K$ is slice. For genus one knots this is of course true; here we present genus two counterexamples.References
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Additional Information
- Charles Livingston
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 193092
- Email: livingst@indiana.edu
- Received by editor(s): August 10, 2000
- Received by editor(s) in revised form: November 10, 2000
- Published electronically: October 12, 2001
- Communicated by: Ronald A. Fintushel
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1551-1555
- MSC (1991): Primary 57M25, 57N70, 57Q60
- DOI: https://doi.org/10.1090/S0002-9939-01-06201-3
- MathSciNet review: 1879982