Concordance of Bing Doubles and Boundary Genus

Abstract

AbstractCha 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 σ, then the n–iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than 2n−1σ. The same result holds with σ replaced by 2τ, twice the Ozsváth–Szabó knot concordance invariant.