Purely cosmetic surgeries and pretzel knots

András I. Stipsicz and Zoltán Szabó

Vol. 313 (2021), No. 1, 195–211

DOI: 10.2140/pjm.2021.313.195

Abstract

We show that all pretzel knots satisfy the (purely) cosmetic surgery conjecture, i.e., Dehn surgeries with different slopes along a (nontrivial) pretzel knot provide different oriented three-manifolds.

Keywords

Cosmetic surgery, pretzel knots, thickness

Mathematical Subject Classification

Primary: 57M50

Milestones

Received: 22 June 2020

Revised: 10 May 2021

Accepted: 12 June 2021

Published: 17 September 2021