Concordance of Bing doubles and boundary genus

TL;DR

This paper establishes lower bounds on the boundary genus of boundary links concordant to iterated Bing doubles of knots with nontrivial signatures, extending previous results on knot concordance and Bing doubles.

Contribution

It proves that iterated Bing doubles of knots with nontrivial signatures cannot be concordant to boundary links with low-genus boundary surfaces, linking knot invariants to boundary genus constraints.

Findings

Nontrivial signature implies high boundary genus for concordant boundary links.

Extends previous results on Bing doubles and knot concordance.

Connects knot invariants with boundary surface genus in link concordance.

Abstract

Cha and Kim proved that if a knot K is not algebraically slice, then no iterated Bing double of K is concordant to the unlink. We prove that if K has nontrivial signature $\sigma$, then the n-iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than $2^{n-1}\sigma$. The same result holds with $\sigma$ replaced by $2\tau$, twice the Ozsvath-Szabo knot concordance invariant.