### Abstract

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 homology groups. Some related results are also obtained.

Original language | English |
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Pages (from-to) | 3955-3971 |

Number of pages | 17 |

Journal | Transactions of the American Mathematical Society |

Volume | 354 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2002 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Blanlœil, V., & Saeki, O. (2002). A theory of concordance for non-spherical 3-knots.

*Transactions of the American Mathematical Society*,*354*(10), 3955-3971. https://doi.org/10.1090/S0002-9947-02-03024-6