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.
@article{hal-00129670,
author = {Blanloeil, Vincent and Saeki, Osamu},
title = {A theory of concordance for non-spherical 3-knots},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00129670}
}
Blanloeil, Vincent; Saeki, Osamu. A theory of concordance for non-spherical 3-knots. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129670/