A theory of concordance for non-spherical 3-knots |
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Authors: | Vincent Blanloeil Osamu Saeki |
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Institution: | Département de Mathématiques, Université Louis Pasteur Strasbourg I, 7 rue René Descartes, 67084 Strasbourg cedex, France ; Faculty of Mathematics, Kyushu University, Hakozaki, Fukuova 812-8581, Japan |
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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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Keywords: | Concordance 3-knot Seifert form algebraic concordance spin structure fibered knot |
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