A theory of concordance for non-spherical 3-knots
Résumé
Consider a closed connected oriented 3-manifold embedded in the $5$-sphere, which is called a $3$-{it knot/} in this paper. For two such knots, we say that their Seifert forms are {it 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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