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On equivariant slice knots
Author(s):
Jae
Choon
Cha;
Ki
Hyoung
Ko
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2175-2182.
MSC (1991):
Primary 57M25, 57M60;
Secondary 57Q60
Posted:
March 1, 1999
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Abstract:
We suggest a method to detect that two periodic knots are not equivariantly concordant, using surgery on factor links. We construct examples which satisfy all known necessary conditions for equivariant slice knots- Naik's and Choi-Ko-Song's improvements of classical results on Seifert forms and Casson-Gordon invariants of slice knots - but are not equivariantly slice.
References:
- 1.
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- 2.
- A. Casson and C. Gordon, On slice knots in dimension three, Proc. Symp. in Pure Math. XXX (1978), part two, 39-53. MR 81g:57003
- 3.
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- 4.
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- 5.
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- 6.
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 , Quart. J. Math. Oxford 34 (1983), 305-322. MR 85d:57004 - 8.
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- 9.
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- 10.
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- 11.
- J. Levine, Knot cobordism group in codimension two, Comm. Math. Helv. 44 (1969), 229-244. MR 39:7618
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- 13.
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- 14.
- S. Naik, Equivariant concordance of knots in
 , Proceedings of Knots 96 (Edited by Shin'ichi Suzuki), World Scientific Publishing Co., 1997, pp 81-89.
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Additional Information:
Jae
Choon
Cha
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon, 305--701, Korea
Email:
jccha@knot.kaist.ac.kr
Ki
Hyoung
Ko
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon, 305--701, Korea
Email:
knot@knot.kaist.ac.kr
DOI:
10.1090/S0002-9939-99-04868-6
PII:
S 0002-9939(99)04868-6
Keywords:
Periodic knot,
concordance
Received by editor(s):
September 21, 1997
Posted:
March 1, 1999
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
1999,
American Mathematical Society
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