Cosmetic surgeries on knots in $S^3$

@article{Ni2010CosmeticSO,
  title={Cosmetic surgeries on knots in \$S^3\$},
  author={Yi Ni and Zhongtao Wu},
  journal={arXiv: Geometric Topology},
  year={2010}
}
  • 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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134 Citations
Highly Influential Citations
22
Background Citations
45
Methods Citations
28
Results Citations
4

134 Citations

Citation Type

Citation Type

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References

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In this paper, we prove that there are no truly cosmetic surgeries on genus one classical knots. If the two surgery slopes have the same sign, we give the only possibilities of reflectively cosmetic…
Cosmetic Surgery in Integral Homology $L$-Spaces
Let $K$ be a non-trivial knot in $S^3$, and let $r$ and $r'$ be two distinct rational numbers of same sign, allowing $r$ to be infinite; we prove that there is no orientation-preserving homeomorphism…
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