Small Dehn surgery and SU(2)
File(s)
Published version
Author(s)
Baldwin, John A
Li, Zhenkun
Sivek, Steven
Ye, Fan
Type
Journal Article
Abstract
We prove that the fundamental group of 3-surgery on a nontrivial knot in S3
always admits an irreducible SU (2)-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-2 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 [3, 5).
always admits an irreducible SU (2)-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-2 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 [3, 5).
Date Issued
2024-07-18
Date Acceptance
2022-09-16
Citation
Geometry and Topology, 2024, 28 (4), pp.1891-1922
ISSN
1364-0380
Publisher
Mathematical Sciences Publishers (MSP)
Start Page
1891
End Page
1922
Journal / Book Title
Geometry and Topology
Volume
28
Issue
4
Copyright Statement
© 2024 The Authors, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.
Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.
License URL
Identifier
https://msp.org/gt/2024/28-4/p07.xhtml
Publication Status
Published