A theory of concordance for non-spherical 3-knots

Vincent Blanlœil, Osamu Saeki
2002 Transactions of the American Mathematical Society  
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
more » ... n free first homology groups. Some related results are also obtained.
doi:10.1090/s0002-9947-02-03024-6 fatcat:w4zt3luokvgqjai2opexcz3hna