Link concordance and generalized doubling operators

TL;DR

This paper introduces a new technique to prove that certain classical knots and links are not slice, including iterated Bing doubles of algebraically slice knots, by defining generalized doubling operators and analyzing their properties.

Contribution

The authors develop generalized doubling operators, including Bing doubling, and demonstrate their nontriviality in detecting non-slice knots without relying on deep analytical bounds.

Findings

Iterated Bing doubles of many algebraically slice knots are not topologically slice.

Generalized doubling operators can detect non-slice boundary links beyond algebraic invariants.

Some proofs avoid using the Cheeger-Gromov bound, simplifying the analysis.

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.