Exceptional Cosmetic surgeries on $S^3$

Abstract

This paper concerns the truly or purely cosmetic surgery conjecture. We give a survey on exceptional surgeries and cosmetic surgeries. We prove that the slope of an exceptional truly cosmetic surgery on a hyperbolic knot in $S^3$ must be $\pm 1$ and the surgery must be toroidal but not Seifert fibred. As consequence we show that there are no exceptional truly cosmetic surgeries on certain types of hyperbolic knot in $S^3$. We also give some properties of Heegaard Floer correction terms and torsion invariants for exceptional cosmetic surgeries on $S^3$.

23 pages

References in corpus (3)

• Floer homology and knot complements
• Surgery formula for the renormalized Euler characteristic of Heegaard Floer homology
• The classification of Toroidal Dehn surgeries on Montesinos knots

Cited by in corpus (3)

• The Legendrian knot complement problem
• $PS{L}_2(\mathbb{C})$-character varieties and Seifert fibered cosmetic surgeries
• Exceptional cosmetic surgeries on homology spheres