Algebraic & Geometric Topology 8 (2008) 1593–1646

DOI: 10.2140/agt.2008.8.1593

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.

Keywords

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

Mathematical Subject Classification

Primary: 57M10, 57M25

References

Publication

Received: 23 January 2008
Revised: 23 July 2008
Accepted: 22 August 2008
Published: 18 September 2008

Authors