Cobordism of exact links

Blanlœil, Vincent; Saeki, Osamu

doi:10.2140/agt.2012.12.1443

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Cobordism of exact links

Vincent Blanlœil and Osamu Saeki

Algebraic & Geometric Topology 12 (2012) 1443–1455

DOI: 10.2140/agt.2012.12.1443

Abstract

A $(2 n - 1)$ –dimensional $(n - 2)$ –connected closed oriented manifold smoothly embedded in the sphere $S^{2 n + 1}$ is called a $(2 n - 1)$ –link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for $n \geq 3$ , two exact $(2 n - 1)$ –links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered $(2 n - 1)$ –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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 57Q45

Secondary: 57Q60, 57R65, 57R40

References

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/

Volume 12, issue 3 (2012)