A theorem of Sanderson on link bordisms in dimension 4

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.