Khovanov homology detects the trefoils
File(s)TrefoilDetection.pdf (651.23 KB)
Accepted version
Author(s)
Baldwin, John A
Sivek, Steven
Type
Journal Article
Abstract
We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer homology and contact geometry. It uses open books; the contact in-variants we defined in the instanton Floer setting; a bypass exact triangle in sutured instanton homology, proven here; and Kronheimer and Mrowka’s spectral sequence relating Khovanov homology with singular instanton knot homology. As a by product, we also strengthen a result of Kronheimer and Mrowka on SU(2) representations of the knot group.
Date Issued
2022-03-15
Date Acceptance
2021-04-12
Citation
Duke Mathematical Journal, 2022, 171 (4), pp.885-956
ISSN
0012-7094
Publisher
Duke University Press
Start Page
885
End Page
956
Journal / Book Title
Duke Mathematical Journal
Volume
171
Issue
4
Copyright Statement
© 2022 Duke University Press.
Identifier
https://arxiv.org/abs/1801.07634
Subjects
General Mathematics
0101 Pure Mathematics
Publication Status
Published
Date Publish Online
2022-03-14