### Abstract

A (2n - 1)-dimensional (n - 2)-connected closed oriented manifold smoothly embedded in the sphere S ^{2n+1} is called a(2n - 1)-link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for n ≥ 3, two exact (2n - 1)-links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered (2n - 1)-links are cobordant if and only if their Seifert forms with respect to their fibers are algebraically cobordant. With this broad class of exact links, we thus clarify the results of Blanloeil [1] concerning cobordisms of odd dimensional nonspherical links.

Original language | English |
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Pages (from-to) | 1443-1455 |

Number of pages | 13 |

Journal | Algebraic and Geometric Topology |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 17 2012 |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Cite this

*Algebraic and Geometric Topology*,

*12*(3), 1443-1455. https://doi.org/10.2140/agt.2012.12.1443

**Cobordism of exact links.** / Blanloeil, Vincent; Saeki, Osamu.

Research output: Contribution to journal › Article

*Algebraic and Geometric Topology*, vol. 12, no. 3, pp. 1443-1455. https://doi.org/10.2140/agt.2012.12.1443

}

TY - JOUR

T1 - Cobordism of exact links

AU - Blanloeil, Vincent

AU - Saeki, Osamu

PY - 2012/7/17

Y1 - 2012/7/17

N2 - A (2n - 1)-dimensional (n - 2)-connected closed oriented manifold smoothly embedded in the sphere S 2n+1 is called a(2n - 1)-link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for n ≥ 3, two exact (2n - 1)-links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered (2n - 1)-links are cobordant if and only if their Seifert forms with respect to their fibers are algebraically cobordant. With this broad class of exact links, we thus clarify the results of Blanloeil [1] concerning cobordisms of odd dimensional nonspherical links.

AB - A (2n - 1)-dimensional (n - 2)-connected closed oriented manifold smoothly embedded in the sphere S 2n+1 is called a(2n - 1)-link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for n ≥ 3, two exact (2n - 1)-links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered (2n - 1)-links are cobordant if and only if their Seifert forms with respect to their fibers are algebraically cobordant. With this broad class of exact links, we thus clarify the results of Blanloeil [1] concerning cobordisms of odd dimensional nonspherical links.

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UR - http://www.scopus.com/inward/citedby.url?scp=84863758324&partnerID=8YFLogxK

U2 - 10.2140/agt.2012.12.1443

DO - 10.2140/agt.2012.12.1443

M3 - Article

AN - SCOPUS:84863758324

VL - 12

SP - 1443

EP - 1455

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 3

ER -