Rational-Slice Knots via Strongly Negative-Amphicheiral Knots |
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Authors: | Kawauchi Akio |
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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. |
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Keywords: | rational-slice knot strongly negative-amphicheiral knot 0-surgery rational cobordism 4-manifold |
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