Rational-Slice Knots via Strongly Negative-Amphicheiral Knots (Communications in Mathematical Research, 2021)
We show that certain satellite knots of every strongly negative-amphicheiralrational knot are rational-slice knots. This proof also shows that the 0-surgery manifold of a certain strongly negative amphicheiral knot such as the figure-eight knotbounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-spheresuch that a second homology class of the 4-manifold is represented by a smoothlyembedded 2-sphere if and only if the modulo two reduction of it is zero.
Keywords: rational-slice knot; strongly negative-amphicheiral knot; 0-surgery; rational cobordism; 4-manifold.