Cosmetic surgeries on knots in $S^3$

By Yi Ni, Zhongtao Wu. 2010

187 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7f2ea14ac230dec68fceee60bdc3218fcecc23a0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Kristen Hendricks
2. Ciprian Manolescu
3. Ian Zemke
4. I. Smith
5. Peter S. Ozsv'ath
6. P. Seidel
7. M. Abouzaid

In Geometry and Topology

1. Kristen Hendricks
2. Ciprian Manolescu
3. Ian Zemke
4. Peter S. Ozsv'ath
5. Zolt'an Szab'o
6. A. Stipsicz
7. Jennifer Hom
8. I. Smith

In Mathematical Physics

1. Kristen Hendricks
2. Ciprian Manolescu
3. Ian Zemke
4. Peter S. Ozsv'ath
5. Jennifer Hom
6. Zolt'an Szab'o
7. A. Stipsicz
8. Sucharit Sarkar

Citations in the corpus

• AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “Another is the work of Ozsv´ath-Szab´o [OS11], Wu [Wu11] and Ni-Wu [NW15] on cosmetic surgeries.”
• Involutive Heegaard Floer homology (2015, methodology): “in the spin structure [0] is given by (1) d(S3 p(K);[0]) = d(L(p;1);0) 2V0(K) = p 1 4 2V0(K); where V0(K) 2Z is an invariant of (smooth) knot concordance, coming from the knot Floer complex of K; cf. [48, 49, 45, 46, 32]. Similarly, using K we obtain new concordance invariants V0(K) and V0(K), and ”