A theorem of Sanderson on link bordisms in dimension 4

Carter, J Scott¹ ; Kamada, Seiichi² ; Saito, Masahico³ ; Satoh, Shin⁴

¹University of South Alabama, Mobile AL 36688, USA
²Osaka City University, Osaka 558-8585, JAPAN
³University of South Florida, Tampa FL 33620, USA
⁴RIMS, Kyoto University, Kyoto, 606-8502

Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 299-310

Résumé

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.

Détail

DOI : 10.2140/agt.2001.1.299

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

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