Corpus ID: 16237529

Rational-Slice Knots via Strongly Negative-amphicheiral Knots

  title={Rational-Slice Knots via Strongly Negative-amphicheiral Knots},
  author={Kawauchi Akio},
  • Kawauchi Akio
  • Published 2009
  • Mathematics
  • 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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