Abstract
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By estimating the knot Floer thickness in terms of the genus and the braid index, we show
that a knot
in
does not admit purely cosmetic surgery whenever
, where
and
denote the genus and the braid index, respectively. In particular, this
establishes the finiteness of purely cosmetic surgeries; for a fixed
, all but finitely many
knots with braid index
satisfies the cosmetic surgery conjecture.
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Keywords
cosmetic surgery, knot Floer thickness, braid index
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Mathematical Subject Classification
Primary: 57K10
Secondary: 57K30
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Publication
Received: 25 April 2021
Revised: 24 November 2021
Accepted: 17 January 2022
Published: 25 July 2023
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© 2023 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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