Volume 8, issue 3 (2008)

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Link concordance and generalized doubling operators

Tim Cochran, Shelly Harvey and Constance Leidy

Algebraic & Geometric Topology 8 (2008) 1593–1646

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.

Bing double, signature, links, concordance, (n)-solvable
Mathematical Subject Classification 2000
Primary: 57M10, 57M25
Received: 23 January 2008
Revised: 23 July 2008
Accepted: 22 August 2008
Published: 18 September 2008
Tim Cochran
Department of Mathematics MS-136
PO Box 1892
Rice University
Houston, TX 77251-1892
Shelly Harvey
Department of Mathematics MS-136
PO Box 1892
Rice University
Houston, TX 77251-1892
Constance Leidy
Department of Mathematics and Computer Science
Wesleyan University
Wesleyan Station
Middletown, CT 06459