Khovanov homology from Floer cohomology
View / Open Files
Authors
Smith, I
Abouzaid, Mohammed
Publication Date
2019Journal Title
Journal of the American Mathematical Society
ISSN
1088-6834
Publisher
American Mathematical Society
Volume
32
Pages
1-79
Type
Article
Metadata
Show full item recordCitation
Smith, I., & Abouzaid, M. (2019). Khovanov homology from Floer cohomology. Journal of the American Mathematical Society, 32 1-79. https://doi.org/10.1090/jams/902
Abstract
This paper realises the Khovanov homology of a link in $ S^3$ as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for the symplectic arc algebra over a field $ \mathbf {k}$ of characteristic zero. Here we prove the symplectic cup and cap bimodules, which relate different symplectic arc algebras, are themselves formal over $ \mathbf {k}$, and we construct a long exact triangle for symplectic Khovanov cohomology. We then prove the symplectic and combinatorial arc algebras are isomorphic over $ \mathbb{Z}$ in a manner compatible with the cup bimodules. It follows that Khovanov cohomology and symplectic Khovanov cohomology co-incide in characteristic zero.
Sponsorship
Engineering and Physical Sciences Research Council (EP/N01815X/1)
Identifiers
External DOI: https://doi.org/10.1090/jams/902
This record's URL: https://www.repository.cam.ac.uk/handle/1810/280001
Rights
Licence:
http://www.rioxx.net/licenses/all-rights-reserved
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.