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Rational-Slice Knots via Strongly Negative-Amphicheiral Knots
Authors:Kawauchi Akio
Abstract:We show that certain satellite knots of every strongly negative-amphicheiral rational 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 knot bounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-sphere such that a second homology class of the 4-manifold is represented by a smoothly embedded 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  
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