vix.ing · top · new · best · stats · spec

On contact cosmetic surgery

2024/11/04 by John B. Etnyre, Etnyre, John B., Tanushree Shah +1
Medicine · Psychology · #57K33 #Body Image and Dysmorphia Studies #FOS: Mathematics #Geometric Topology (math.GT) #Medical and Biological Sciences #Surgical Sutures and Adhesives #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2411.02201

openalex publication_date 2024/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate that the contact cosmetic surgery conjecture holds true for all non-trivial Legendrian knots, with the possible exception of Lagrangian slice knots. We also discuss the contact cosmetic surgeries on Legendrian unknots and make the surprising observation that there are some Legendrian unknots that have a contact surgery with no cosmetic pair, while all other contact surgeries are contactomorphic to infinitely many other contact surgeries on the knot.

Related