### 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 |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*354*(10), 3955-3971. https://doi.org/10.1090/S0002-9947-02-03024-6

**A theory of concordance for non-spherical 3-knots.** / Blanlœil, Vincent; Saeki, Osamu.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 354, no. 10, pp. 3955-3971. https://doi.org/10.1090/S0002-9947-02-03024-6

}

TY - JOUR

T1 - A theory of concordance for non-spherical 3-knots

AU - Blanlœil, Vincent

AU - Saeki, Osamu

PY - 2002/10/1

Y1 - 2002/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036787947&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036787947&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-02-03024-6

DO - 10.1090/S0002-9947-02-03024-6

M3 - Article

VL - 354

SP - 3955

EP - 3971

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 10

ER -