Geodesic
Cobordism of exact links
Blanlœil, Vincent1 ; Saeki, Osamu2
1IRMA Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg cedex, France
2Institute of Mathematics for Industry, Kyushu University, Motoka 744, Fukuoka 819-0395, Japan
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1443-1455
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A (2n − 1)–dimensional (n − 2)–connected closed oriented manifold smoothly embedded in the sphere S2n+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 Blanlœil [Ann. Fac. Sci. Toulouse Math. 7 (1998) 185–205] concerning cobordisms of odd dimensional nonspherical links.

DOI : 10.2140/agt.2012.12.1443
Classification : 57Q45, 57Q60, 57R65, 57R40
Keywords: high dimensional knot, knot cobordism, Seifert form, algebraic cobordism, nonspherical link, fibered link

Blanlœil, Vincent  1   ; Saeki, Osamu  2

1 IRMA Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg cedex, France
2 Institute of Mathematics for Industry, Kyushu University, Motoka 744, Fukuoka 819-0395, Japan 
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Blanlœil, Vincent; Saeki, Osamu. Cobordism of exact links. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1443-1455. doi: 10.2140/agt.2012.12.1443

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