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dc.contributor.authorSmith, Ivan
dc.contributor.authorAbouzaid, Mohammed
dc.date.accessioned2018-09-10T22:14:46Z
dc.date.available2018-09-10T22:14:46Z
dc.date.issued2019-01
dc.identifier.issn1088-6834
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/280001
dc.description.abstractThis 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.
dc.publisherAmerican Mathematical Society
dc.titleKhovanov homology from Floer cohomology
dc.typeArticle
prism.endingPage79
prism.publicationNameJournal of the American Mathematical Society
prism.startingPage1
prism.volume32
dc.identifier.doi10.17863/CAM.27367
dcterms.dateAccepted2018-05-23
rioxxterms.versionofrecord10.1090/jams/902
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2018-05-23
dc.identifier.eissn1088-6834
rioxxterms.typeJournal Article/Review
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/N01815X/1)
cam.issuedOnline2018-07-27


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