Kauffman's conjecture on surgery curves of genus one slice knots

A knot is a smooth embedding $\mathbb{S}^1\hookrightarrow\mathbb{S}^3=\partial\mathbb{B}^4$. It is slice if it bounds a smoothly embedded disk in $\mathbb{B}^4$. A genus one Seifert surface for a knot $K$ is an embedded oriented punctured torus $F\subset\mathbb{S}^3$ with boundary $K$. A surgery curve for $F$ is a homologically essential simple closed curve on $F$ with self-linking zero with respect to the Seifert form on $F$. Kauffman's conjecture. $K$ is a slice knot with a genus one Seifert surface $F$ if and only if $F$ has a surgery curve which is slice. Kauffman's conjecture proposed a converse to the fact that a slice surgery curve on a genus one Seifert surface allows one to construct a slice disk for the boundary knot by surgery. It was disproved by Cochran and Davis soon after the paper was completed.