Algebraic & Geometric Topology

Cobordism of exact links

Vincent Blanlœil and Osamu Saeki

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Abstract

A (2n1)–dimensional (n2)–connected closed oriented manifold smoothly embedded in the sphere S2n+1 is called a (2n1)–link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for n3, two exact (2n1)–links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered (2n1)–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.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 3 (2012), 1443-1455.

Dates
Received: 17 November 2011
Revised: 16 March 2012
Accepted: 23 March 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715404

Digital Object Identifier
doi:10.2140/agt.2012.12.1443

Mathematical Reviews number (MathSciNet)
MR2966692

Zentralblatt MATH identifier
1250.57038

Subjects
Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Secondary: 57Q60: Cobordism and concordance 57R65: Surgery and handlebodies 57R40: Embeddings

Keywords
high dimensional knot knot cobordism Seifert form algebraic cobordism nonspherical link fibered link

Citation

Blanlœil, Vincent; Saeki, Osamu. Cobordism of exact links. Algebr. Geom. Topol. 12 (2012), no. 3, 1443--1455. doi:10.2140/agt.2012.12.1443. https://projecteuclid.org/euclid.agt/1513715404


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References

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