A theorem of Sanderson on link bordisms in dimension 4

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

References

Forward citations

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

Volume 1, issue 1 (2001)

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