New examples of nonslice, algebraically slice knots
Author:
Charles Livingston
Journal:
Proc. Amer. Math. Soc. 130 (2002), 15511555
MSC (1991):
Primary 57M25, 57N70, 57Q60
Published electronically:
October 12, 2001
MathSciNet review:
1879982
Fulltext PDF Free Access
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Abstract: For , if the Seifert form of a knotted sphere in has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three. However, in the threedimensional case it is true that if the metabolizer has a basis represented by a strongly slice link, then 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 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/S0002993901062013
PII:
S 00029939(01)062013
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
