A Theorem of Sanderson on Link Bordisms in Dimension 4

J. Scott Carter; Seiichi Kamada; Masahico Saito; Shin Satoh

doi:10.2140/agt.2001.1.299

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A Theorem of Sanderson on Link Bordisms in Dimension 4

J. Scott Carter·Seiichi Kamada·Masahico Saito·Shin Satoh

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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.

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J. Scott Carter, Seiichi Kamada, Masahico Saito, Shin Satoh. 2000-08-14. A Theorem of Sanderson on Link Bordisms in Dimension 4. https://doi.org/10.2140/agt.2001.1.299

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