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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A theory of concordance for non-spherical 3-knots


Authors: Vincent Blanloeil and Osamu Saeki
Journal: Trans. Amer. Math. Soc. 354 (2002), 3955-3971
MSC (2000): Primary 57Q45; Secondary 57R40
Published electronically: May 21, 2002
MathSciNet review: 1926861
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Abstract: Consider a closed connected oriented 3-manifold embedded in the $5$-sphere, which is called a $3$-knot in this paper. For two such knots, we say that their Seifert forms are spin concordant, if they are algebraically concordant with respect to a diffeomorphism between the 3-manifolds which preserves their spin structures. Then we show that two simple fibered 3-knots are geometrically concordant if and only if they have spin concordant Seifert forms, provided that they have torsion free first homology groups. Some related results are also obtained.


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Additional Information

Vincent Blanloeil
Affiliation: Département de Mathématiques, Université Louis Pasteur Strasbourg I, 7 rue René Descartes, 67084 Strasbourg cedex, France
Email: blanloeil@math.u-strasbg.fr

Osamu Saeki
Affiliation: Faculty of Mathematics, Kyushu University, Hakozaki, Fukuova 812-8581, Japan
Email: saeki@math.kyushu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03024-6
PII: S 0002-9947(02)03024-6
Keywords: Concordance, 3-knot, Seifert form, algebraic concordance, spin structure, fibered knot
Received by editor(s): May 12, 2001
Received by editor(s) in revised form: February 15, 2002
Published electronically: May 21, 2002
Additional Notes: The second author has been supported in part by Grant-in-Aid for Scientific Research (No. 11440022), Ministry of Education, Science and Culture, Japan, and was supported in part by Louis Pasteur University, France, during his stay there in September 2000.
Article copyright: © Copyright 2002 American Mathematical Society