Vol. 313, No. 1, 2021

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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
Authors
András I. Stipsicz
Rényi Institute of Mathematics
Budapest
Hungary
Zoltán Szabó
Department of Mathematics
Princeton University
Princeton, NJ
United States