Counterexamples to Kauffman's conjectures on slice knots

Smooth slice boundary links whose derivative links have nonvanishing Milnor invariants

“…The curves a i in Figure 8 are unknots, so the components individually satisfy the strong Kauffman conjecture that there is a slice metaboliser. Once again, Figure 8 comes from [CD13], this time their Figure 10, and we include it here for the benefit of the reader. …”

“…In [CD13,Section 7], it is claimed that the Seifert surface for their knot stabilises to a surface with a slice derivative link, although details are not given in their preprint. We thank Chris Davis for helpful discussions concerning this.…”

“…Lemma 3.2 (Link version of Theorem 3.1 of [CD13]). Let R be a slice link bounding slice discs D in the 4-ball B 4 .…”

“…We were inspired by the recent work of T. Cochran and C. W. Davis [CD13]. They found counterexamples to the thirty year old Kauffman conjecture, which was that any genus one slice knot has a genus one Seifert surface on which there is a metabolising curve J which has Arf(J) = 0.…”

“…Section 2 recalls some relevant definitions. Section 3 generalises a result of [CD13] to the case of infection by string links, which shows that a certain operation on a slice link yields another slice link. Section 4 proves a formula detailing how the Milnor invariants change under infection by a string link.…”