#### Volume 12, issue 3 (2012)

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Cobordism of exact links

### Vincent Blanlœil and Osamu Saeki

Algebraic & Geometric Topology 12 (2012) 1443–1455
##### Abstract

A $\left(2n-1\right)$–dimensional $\left(n-2\right)$–connected closed oriented manifold smoothly embedded in the sphere ${S}^{2n+1}$ is called a $\left(2n-1\right)$–link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for $n\ge 3$, two exact $\left(2n-1\right)$–links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered $\left(2n-1\right)$–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 Blanlœil [Ann. Fac. Sci. Toulouse Math. 7 (1998) 185–205] concerning cobordisms of odd dimensional nonspherical links.

##### Keywords
high dimensional knot, knot cobordism, Seifert form, algebraic cobordism, nonspherical link, fibered link
##### Mathematical Subject Classification 2010
Primary: 57Q45
Secondary: 57Q60, 57R65, 57R40
##### Publication
Received: 17 November 2011
Revised: 16 March 2012
Accepted: 23 March 2012
Published: 3 July 2012
##### Authors
 Vincent Blanlœil IRMA Université de Strasbourg 7, rue René Descartes 67084 Strasbourg cedex France http://www-irma.u-strasbg.fr/~blanloei/ Osamu Saeki Institute of Mathematics for Industry Kyushu University Motoka 744 Fukuoka 819-0395 Japan http://imi.kyushu-u.ac.jp/~saeki/