Volume 6, issue 5 (2006)

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Slicing Bing doubles

David Cimasoni

Algebraic & Geometric Topology 6 (2006) 2395–2415
 arXiv: math.GT/0609458
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.