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 Aββ-algebra associated to the (k,k)-nilpotent slice ykβ obtained by counting holomorphic discs which satisfy a suitable conormal condition at infinity in a partial compactification yΛβkβ. The space yΛβkβ is obtained as the Hilbert scheme of a partial compactification of the A2kβ1β-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.This is the author accepted manuscript. The final version is available from Duke University Press via http://dx.doi.org/10.1215/00127094-344945
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