English

Families of cosmetic surgeries

Geometric Topology 2026-04-06 v1

Abstract

We construct infinite families of chirally cosmetic surgeries on chiral hyperbolic knots and purely cosmetic surgeries on hyperbolic manifolds with multiple cusps, disproving conjectures that these phenomena do not appear, including Problem 1.12(d) in the K3 problem list. We also give some hints regarding why chirally cosmetic surgeries appear to be more common than purely cosmetic surgeries on 11-cusped manifolds.

Keywords

Cite

@article{arxiv.2604.02672,
  title  = {Families of cosmetic surgeries},
  author = {Qiuyu Ren},
  journal= {arXiv preprint arXiv:2604.02672},
  year   = {2026}
}

Comments

8 pages, 1 figure