Slicing Bing doubles

Abstract

Bing doubling is an operation which produces a 2–component boundary link $B\left(K\right)$ from a knot $K$. If $K$ is slice, then $B\left(K\right)$ is easily seen to be boundary slice. In this paper, we investigate whether the converse holds. Our main result is that if $B\left(K\right)$ is boundary slice, then $K$ is algebraically slice. We also show that the Rasmussen invariant can tell that certain Bing doubles are not smoothly slice.