Algebraic & Geometric Topology 12 (2012) 1443–1455

DOI: 10.2140/agt.2012.12.1443

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

Primary: 57Q45

Secondary: 57Q60, 57R40, 57R65

References

Publication

Received: 17 November 2011
Revised: 16 March 2012
Accepted: 23 March 2012
Published: 3 July 2012

Authors