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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
Mathematical Subject Classification 2000
Primary: 57Q45
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Publication
Received: 9 October 2000
Revised: 11 May 2001
Accepted: 17 May 2001
Published: 23 May 2001
Authors
J Scott Carter
University of South Alabama
Mobile AL 36688
USA
Seiichi Kamada
Osaka City University
Osaka 558-8585
JAPAN
Masahico Saito
University of South Florida
Tampa FL 33620
USA
Shin Satoh
RIMS, Kyoto University, Kyoto, 606-8502