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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

New examples of non-slice, algebraically slice knots


Author: Charles Livingston
Journal: Proc. Amer. Math. Soc. 130 (2002), 1551-1555
MSC (1991): Primary 57M25, 57N70, 57Q60
Published electronically: October 12, 2001
MathSciNet review: 1879982
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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.


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Additional Information

Charles Livingston
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: livingst@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06201-3
PII: S 0002-9939(01)06201-3
Keywords: Knot concordance, algebraically slice
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
Article copyright: © Copyright 2001 American Mathematical Society