Algebraic & Geometric Topology

Link concordance and generalized doubling operators

Tim Cochran, Shelly Harvey, and Constance Leidy

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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.

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1593-1646.

Dates
Received: 23 January 2008
Revised: 23 July 2008
Accepted: 22 August 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796899

Digital Object Identifier
doi:10.2140/agt.2008.8.1593

Mathematical Reviews number (MathSciNet)
MR2443256

Zentralblatt MATH identifier
1190.57010

Subjects
Primary: 57M10: Covering spaces 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Bing double signature links concordance (n)-solvable

Citation

Cochran, Tim; Harvey, Shelly; Leidy, Constance. Link concordance and generalized doubling operators. Algebr. Geom. Topol. 8 (2008), no. 3, 1593--1646. doi:10.2140/agt.2008.8.1593. https://projecteuclid.org/euclid.agt/1513796899


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