Khovanov homology and the cinquefoil
File(s)KhT25.pdf (387.85 KB)
Accepted version
Author(s)
Baldwin, John A
Hu, Ying
Sivek, Steven
Type
Journal Article
Abstract
We prove that Khovanov homology with coefficients in Z/2Z detects the (2, 5)
torus knot. Our proof makes use of a wide range of deep tools in Floer homology, Khovanov homology, and Khovanov homotopy. We combine these tools with classical results on the dynamics of surface homeomorphisms to reduce the detection question to a problem about mutually braided unknots, which we then solve with computer assistance.
torus knot. Our proof makes use of a wide range of deep tools in Floer homology, Khovanov homology, and Khovanov homotopy. We combine these tools with classical results on the dynamics of surface homeomorphisms to reduce the detection question to a problem about mutually braided unknots, which we then solve with computer assistance.
Date Issued
2025
Date Acceptance
2022-01-26
Citation
Journal of the European Mathematical Society, 2025, 27 (6), pp.2443-2465
ISSN
1435-9855
Publisher
EMS Press
Start Page
2443
End Page
2465
Journal / Book Title
Journal of the European Mathematical Society
Volume
27
Issue
6
Copyright Statement
© 2024 European Mathematical Society. Published by EMS Press
Identifier
https://arxiv.org/abs/2105.12102
Publication Status
Published
Date Publish Online
2024-01-09