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A remark on the finiteness of purely cosmetic surgeries

Tetsuya Ito

Algebraic & Geometric Topology 23 (2023) 2213–2219
Abstract

By estimating the knot Floer thickness in terms of the genus and the braid index, we show that a knot K in S3 does not admit purely cosmetic surgery whenever g(K) 3 2b(K), where g(K) and b(K) denote the genus and the braid index, respectively. In particular, this establishes the finiteness of purely cosmetic surgeries; for a fixed b, all but finitely many knots with braid index b satisfies the cosmetic surgery conjecture.

Keywords
cosmetic surgery, knot Floer thickness, braid index
Mathematical Subject Classification
Primary: 57K10
Secondary: 57K30
References
Publication
Received: 25 April 2021
Revised: 24 November 2021
Accepted: 17 January 2022
Published: 25 July 2023
Authors
Tetsuya Ito
Department of Mathematics
Graduate School of Science
Kyoto University
Kyoto
Japan

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