Volume 1, issue 1 (2001)

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A theorem of Sanderson on link bordisms in dimension 4

J Scott Carter, Seiichi Kamada, Masahico Saito and Shin Satoh

Algebraic & Geometric Topology 1 (2001) 299–310
 arXiv: math.GT/0008099
Abstract

The groups of link bordism can be identified with homotopy groups via the Pontryagin–Thom construction. B J Sanderson computed the bordism group of 3 component surface-links using the Hilton–Milnor Theorem, and later gave a geometric interpretation of the groups in terms of intersections of Seifert hypersurfaces and their framings. In this paper, we geometrically represent every element of the bordism group uniquely by a certain standard form of a surface-link, a generalization of a Hopf link. The standard forms give rise to an inverse of Sanderson’s geometrically defined invariant.

Keywords
surface links, link bordism groups, triple linking, Hopf $2$–links
Primary: 57Q45