  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-infinity algebra associated to the
(k,k)-nilpotent slice Y, obtained by counting holomorphic discs which satisfy a
suitable conormal condition at infinity in a partial compactification of Y. The
partial compactification is obtained as the Hilbert scheme of a partial
compactification of a Milnor fibre. 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.
