Link concordance and generalized doubling operators

Cochran, Tim¹ ; Harvey, Shelly¹ ; Leidy, Constance²

¹Department of Mathematics MS-136, PO Box 1892, Rice University, Houston, TX 77251-1892, USA
²Department of Mathematics and Computer Science, Wesleyan University, Wesleyan Station, Middletown, CT 06459, USA

Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1593-1646

Résumé

We introduce a technique for showing classical knots and links are not slice. As one application we show that the iterated Bing doubles of many algebraically slice knots are not topologically slice. Some of the proofs do not use the existence of the Cheeger–Gromov bound, a deep analytical tool used by Cochran–Teichner. We define generalized doubling operators, of which Bing doubling is an instance, and prove our nontriviality results in this more general context. Our main examples are boundary links that cannot be detected in the algebraic boundary link concordance group.

Détail

DOI : 10.2140/agt.2008.8.1593

Keywords: Bing double, signature, links, concordance, (n)-solvable

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