Link concordance and generalized doubling operators

Details Link concordance and generalized doubling operators Link concordance and generalized doubling operators

2008-01-23

arxiv.org/abs/0801.3677v2

Alg. Geom. Topology, 8(2008), 1593-1646

Mathematics

Geometric Topology

45 pages. Final version. Changed figures 1.3 and 4.2. Expanded Remark 5.4. Fixed typos and made other minor changes. Some of t

Scientific paper

10.2140/agt.2008.8.1593

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.

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