Volume 12, issue 3 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Cobordism of exact links

Vincent Blanlœil and Osamu Saeki

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

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.

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/