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Two-bridge knots admit
no purely cosmetic surgeries
Kazuhiro Ichihara, In Dae Jong, Thomas W Mattman and Toshio Saito |
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Algebraic & Geometric Topology 21 (2021) 2411–2424
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Abstract |
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We show that two-bridge knots and alternating fibered knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce –manifolds that are homeomorphic as oriented manifolds. Our argument, based on a recent result by Hanselman, uses several invariants of knots or –manifolds; for knots, we study the signature and some finite type invariants, and for –manifolds, we deploy the Casson invariant. |
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Dedicated to Professor Hitoshi Murakami on his 60th birthday |
Keywords
alternating knot, fibered knot, two-bridge knot, pretzel
knot, cosmetic surgery, signature, finite type invariant,
$\mathrm{SL}(2,C)$ Casson invariant
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25
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References |
Publication
Received: 5 September 2019
Revised: 17 January 2020
Accepted: 4 October 2020
Published: 31 October 2021
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Authors |
| Kazuhiro Ichihara | |
| Department of Mathematics College of Humanities and Sciences Nihon University Tokyo Japan |
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| http://www.math.chs.nihon-u.ac.jp/~ichihara/index.html | |
| In Dae Jong | |
| Department of Mathematics Kindai University Osaka Japan |
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| Thomas W Mattman | |
| Department of Mathematics and
Statistics California State University at Chico Chico, CA United States |
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| Toshio Saito | |
| Department of Mathematics Joetsu University of Education Joetsu Japan |
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