Algebraic & Geometric Topology

A theorem of Sanderson on link bordisms in dimension 4

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

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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.

Article information

Algebr. Geom. Topol., Volume 1, Number 1 (2001), 299-310.

Received: 9 October 2000
Revised: 11 May 2001
Accepted: 17 May 2001
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}

surface links link bordism groups triple linking Hopf $2$–links


Carter, J Scott; Kamada, Seiichi; Saito, Masahico; Satoh, Shin. A theorem of Sanderson on link bordisms in dimension 4. Algebr. Geom. Topol. 1 (2001), no. 1, 299--310. doi:10.2140/agt.2001.1.299.

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