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

DOI:
https://doi.org/10.1090/S0002-9947-02-03024-6

Published electronically:
May 21, 2002

MathSciNet review:
1926861

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider a closed connected oriented 3-manifold embedded in the -sphere, which is called a -*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:
https://doi.org/10.1090/S0002-9947-02-03024-6

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