English

On The Virtual Cosmetic Surgery Conjecture

Geometric Topology 2021-10-12 v5

Abstract

Let K be a knot in S^3, and M and M' be distinct Dehn surgeries along K. We investigate when M covers M'. When K is a torus knot, we provide a complete classification of such covers. When K is a hyperbolic knot, we provide partial results in the direction of the conjecture that M never covers M'.

Keywords

Cite

@article{arxiv.1701.02361,
  title  = {On The Virtual Cosmetic Surgery Conjecture},
  author = {Keegan Boyle},
  journal= {arXiv preprint arXiv:1701.02361},
  year   = {2021}
}

Comments

Corrected Theorem 2 (and its proof) by adding a necessary condition that was missing. Thanks to Tye Lidman for pointing out the error

R2 v1 2026-06-22T17:45:19.411Z