Link concordance and generalized doubling operators

Abstract

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.

45 pages. Final version. Changed figures 1.3 and 4.2. Expanded Remark 5.4. Fixed typos and made other minor changes. Some of the results are renumbered. Updates references. Note: All results except Cor. 4.8, Ex. 4.4, Ex. 4.6, Lemmas 6.4, 6.5 appeared previously in 0705.3987 under different title: Knot concordance and Blanchfield duality

References in corpus (1)

• Slicing Bing doubles

Cited by in corpus (9)

• Knot Concordance and Higher-Order Blanchfield Duality
• Filtering smooth concordance classes of topologically slice knots
• Primary decomposition and the fractal nature of knot concordance
• Derivatives of Knots and Second-order Signatures
• Grope metrics on the knot concordance set
• Topological concordance of knots in homology spheres and the solvable filtration
• Concordance of Bing doubles and boundary genus
• Whitney towers, Gropes and Casson-Gordon style invariants of links
• Linear independence of cables in the knot concordance group