A theory of concordance for non-spherical 3-knots
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- by Vincent Blanlœil and Osamu Saeki PDF
- Trans. Amer. Math. Soc. 354 (2002), 3955-3971 Request permission
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.References
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Additional Information
- Vincent Blanlœil
- 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
- 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.
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 3955-3971
- MSC (2000): Primary 57Q45; Secondary 57R40
- DOI: https://doi.org/10.1090/S0002-9947-02-03024-6
- MathSciNet review: 1926861