## Publication: The symplectic arc algebra is formal

 dc.contributor.author Abouzaid, Mohammed dc.contributor.author Smith, Ivan dc.date.accessioned 2019-04-26T08:57:22Z dc.date.available 2019-04-26T08:57:22Z dc.date.issued 28/01/16 dc.description We 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.uri https://demo7.dspace.org/handle/10673/469 dc.language en dc.publisher Duke University Press dc.title The symplectic arc algebra is formal dspace.entity.type Publication relation.isProjectOfPublication 554e1b58-c73a-4cc1-bc2d-76ea953320f4 relation.isProjectOfPublication.latestForDiscovery 554e1b58-c73a-4cc1-bc2d-76ea953320f4