Algebraic and Geometric Topology 1 (2001), paper no. 14, pages 299-310.

A theorem of Sanderson on link bordisms in dimension 4

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

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

AMS subject classification. Primary: 57Q45 .

DOI: 10.2140/agt.2001.1.299

E-print: arXiv:math.GT/0008099

Submitted: 9 October 2000. (Revised: 11 May 2001.) Accepted: 17 May 2001. Published: 23 May 2001.

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

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

Email: carter@mathstat.usouthal.edu, kamada@sci.osaka-cu.ac.jp, saito@math.usf.edu, satoh@kurims.kyoto-u.ac.jp

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