SU(2)-cyclic surgeries and the pillowcase
File(s)
Accepted version
Author(s)
Sivek, Steven
Zentner, Raphael
Type
Journal Article
Abstract
We study knots in S3 with infinitely many SU(2)-cyclic surgeries, which are Dehn surgeries such that every representation of the resulting fundamental group into SU(2) has cyclic image. We show that for every such nontrivial knot K, its set of SU(2)-cyclic slopes is bounded and has a unique limit point, which is both a rational number and a boundary slope for K. We also show that such knots are prime and have infinitely many instanton L‑space surgeries. Our methods include the application of holonomy perturbation techniques to instanton knot homology, using a strengthening of recent work by the second author.
Date Issued
2022-05-01
Date Acceptance
2020-01-27
Citation
Journal of Differential Geometry, 2022, 121 (1), pp.101-185
ISSN
0022-040X
Publisher
International Press
Start Page
101
End Page
185
Journal / Book Title
Journal of Differential Geometry
Volume
121
Issue
1
Copyright Statement
© 2022 Lehigh University
Identifier
http://arxiv.org/abs/1710.01957v1
Subjects
math.GT
math.GT
Notes
62 pages, 6 figures
Publication Status
Published