New examples of non–slice, algebraically slice knots

Abstract:

For $n >1$, if the Seifert form of a knotted $2n-1$–sphere $K$ in $S^{2n+ 1}$ has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three. However, in the three–dimensional case it is true that if the metabolizer has a basis represented by a strongly slice link, then $K$ is slice. The question has been asked as to whether it is sufficient that each basis element is represented by a slice knot to assure that $K$ is slice. For genus one knots this is of course true; here we present genus two counterexamples.