Show simple item record

dc.contributor.authorAbouzaid, Mohammeden
dc.contributor.authorSmith, Ivanen
dc.date.accessioned2016-06-07T09:30:02Z
dc.date.available2016-06-07T09:30:02Z
dc.date.issued2016-01-28en
dc.identifier.issn0012-7094
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/256187
dc.description.abstractWe prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degree-one Hochschild cohomology class on a Floer A$_\infty$-algebra associated to the ($k$,$k$)-nilpotent slice $y_k$ obtained by counting holomorphic discs which satisfy a suitable conormal condition at infinity in a partial compactification $\bar y$$_k$. The space $\bar y$$_k$ is obtained as the Hilbert scheme of a partial compactification of the A$_{2k-1}$-Milnor fiber. A sequel to this paper will prove formality of the symplectic cup and cap bimodules and infer that symplectic Khovanov cohomology and Khovanov cohomology have the same total rank over characteristic zero fields.
dc.languageEnglishen
dc.language.isoenen
dc.publisherDuke University Press
dc.subjectsymplectic topologyen
dc.subjectKhovanov homologyen
dc.subjectFukaya categoryen
dc.subjectnilpotent sliceen
dc.titleThe symplectic arc algebra is formalen
dc.typeArticle
dc.description.versionThis is the author accepted manuscript. The final version is available from Duke University Press via http://dx.doi.org/10.1215/00127094-3449459en
prism.endingPage1060
prism.publicationDate2016en
prism.publicationNameDuke Mathematical Journalen
prism.startingPage985
prism.volume165en
dc.identifier.doi10.17863/CAM.128
dcterms.dateAccepted2015-07-07en
rioxxterms.funderNational Science Foundationen
rioxxterms.identifier.projectDMS-1308179en
rioxxterms.versionofrecord10.1215/00127094-3449459en
rioxxterms.versionAMen
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2016-01-28en
rioxxterms.typeJournal Article/Reviewen
rioxxterms.funder.project0e75602a-ad3a-444a-823f-d971ce8ebe43en


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record