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Small Dehn surgery and
$\mathrm{SU}(2)$
John A Baldwin, Zhenkun Li, Steven Sivek and Fan Ye |
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Geometry & Topology 28 (2024) 1891–1922
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Abstract |
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We prove that the fundamental group of –surgery on a nontrivial knot in always admits an irreducible –representation. This answers a question of Kronheimer and Mrowka dating from their work on the property P conjecture. An important ingredient in our proof is a relationship between instanton Floer homology and the symplectic Floer homology of genus- surface diffeomorphisms, due to Ivan Smith. We use similar arguments at the end to extend our main result to infinitely many surgery slopes in the interval . |
Keywords
instanton, $\mathrm{SU}(2)$, Floer homology,
representations, knots, fundamental group
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Mathematical Subject Classification
Primary: 57K10, 57K18, 57M05
Secondary: 57K20, 57K33
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References |
Publication
Received: 9 October 2021
Revised: 19 August 2022
Accepted: 16 September 2022
Published: 18 July 2024
Proposed: Ciprian Manolescu
Seconded: Cameron Gordon, András I Stipsicz
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Authors |
| John A Baldwin | |
| Department of Mathematics Boston College Chestnut Hill, MA United States |
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| Zhenkun Li | |
| Department of Mathematics Stanford University Stanford, CA United States |
School of Mathematics and
Statistics University of South Florida Tampa, FL United States |
| Steven Sivek | |
| Department of Mathematics Imperial College London London United Kingdom |
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| Fan Ye | |
| Department of Pure Mathematics and
Mathematical Statistics University of Cambridge Cambridge United Kingdom |
Department of Mathematics Harvard University Cambridge, MA United States |
| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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