Instantons and L-space surgeries
File(s)
Published version
Author(s)
Baldwin, John A
Sivek, Steven
Type
Journal Article
Abstract
We prove that instanton L-space knots are fibered and strongly quasi positive. Our proof differs conceptually from proofs of the analogous result in Heegaard Floer homology, and includes a new decomposition theorem for cobordism maps in framed instant on Floer homology akin to the Spin$c$ decompositions of cobordism maps in other Floer homology theories. As our main application, we prove (modulo a mild nondegeneracy condition)that for r a positive rational number and Ka nontrivial knot in the 3-sphere, there exists an irreducible homomorphismπ1(S3r(K))→SU(2)unlessr≥2g(K)−1 and Kis both fibered and strongly quasi positive, broadly generalizing results of Kronheimer and Mrowka. We also answer a question of theirs from 2004, proving that there is always an irreducible homomorphism from the fundamental group of 4-surgeryon a nontrivial knot to SU(2). In another application, we show that a slight enhancement of the A-polynomial detects infinitely many torus knots, including the trefoil.
Date Issued
2022-10-06
Date Acceptance
2021-04-08
Citation
Journal of the European Mathematical Society, 2022, 25 (10), pp.4033-4122
ISSN
1435-9855
Publisher
European Mathematical Society
Start Page
4033
End Page
4122
Journal / Book Title
Journal of the European Mathematical Society
Volume
25
Issue
10
Copyright Statement
©2022 European Mathematical Society. Published by EMS Press and licensed under a CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/)
License URL
Publication Status
Published
Date Publish Online
2022-10-06