Cosmetic surgeries on knots in $S^3$

  title={Cosmetic surgeries on knots in \$S^3\$},
  author={Yi Ni and Zhongtao Wu},
  journal={arXiv: Geometric Topology},
  • Yi Ni, Zhongtao Wu
  • Published 23 September 2010
  • Mathematics, Medicine
  • arXiv: Geometric Topology
Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$, we show that the two surgery slopes must be the opposite of each other. One ingredient of our proof is a Dehn surgery formula for correction terms in Heegaard Floer homology. 
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  • R. Tao
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    Journal of Knot Theory and Its Ramifications
  • 2019
Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that nontrivial knots in [Formula: see text] do not
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