Kauffman's derivative-sliceness conjecture for slice knots

Let KK be a knot with a slice disk Δ\Delta, and let JJ be a derivative of KK associated to Δ\Delta. Kauffman's conjecture. If KK is a slice knot via Δ\Delta, then JJ is a slice link.

This is the converse of the elementary fact that a slice derivative yields a slice disk for KK. The conjecture is disproved by a counterexample consisting of a genus-one slice knot with a non-slice associated derivative.

Sources & referencesView supporting material

Primary source

Tim Cochran and Christopher William Davis, “Cut open null-bordisms and derivatives of slice knots”, arXiv:1511.07295 (2016).

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