A Theorem of Sanderson on Link Bordisms in Dimension 4

Details A Theorem of Sanderson on Link Bordisms in Dimension 4 A Theorem of Sanderson on Link Bordisms in Dimension 4

2000-08-14

arxiv.org/abs/math/0008099v2

Algebr. Geom. Topol. 1 (2001) 299-310

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-14.abs.html

Scientific paper

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.

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