dc.contributor.author Smith, Ivan dc.contributor.author Abouzaid, Mohammed dc.date.accessioned 2018-09-10T22:14:46Z dc.date.available 2018-09-10T22:14:46Z dc.date.issued 2019-01 dc.identifier.issn 1088-6834 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/280001 dc.description.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. dc.publisher American Mathematical Society dc.title Khovanov homology from Floer cohomology dc.type Article prism.endingPage 79 prism.publicationName Journal of the American Mathematical Society prism.startingPage 1 prism.volume 32 dc.identifier.doi 10.17863/CAM.27367 dcterms.dateAccepted 2018-05-23 rioxxterms.versionofrecord 10.1090/jams/902 rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2018-05-23 dc.identifier.eissn 1088-6834 rioxxterms.type Journal Article/Review pubs.funder-project-id Engineering and Physical Sciences Research Council (EP/N01815X/1) cam.issuedOnline 2018-07-27
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