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The symplectic arc algebra is formal

dc.contributor.authorAbouzaid, Mohammed
dc.contributor.authorSmith, Ivan
dc.date.accessioned2019-04-26T08:57:22Z
dc.date.available2019-04-26T08:57:22Z
dc.date.issued28/01/16
dc.descriptionWe 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.identifier.urihttps://demo7.dspace.org/handle/10673/469
dc.languageen
dc.publisherDuke University Press
dc.titleThe symplectic arc algebra is formal
dspace.entity.typePublication
relation.isProjectOfPublication554e1b58-c73a-4cc1-bc2d-76ea953320f4
relation.isProjectOfPublication.latestForDiscovery554e1b58-c73a-4cc1-bc2d-76ea953320f4
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