Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 3 (2012), 1443-1455.
Cobordism of exact links
A –dimensional –connected closed oriented manifold smoothly embedded in the sphere is called a –link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for , two exact –links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered –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.
Algebr. Geom. Topol., Volume 12, Number 3 (2012), 1443-1455.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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