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A simple proof of a theorem of Fukaya and Oh
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abstract
We study the moduli space of pseudo pointed holomorphic disks with boundaries mapped in the zero section of the cotangent bundle of a manifold. We define perturbations of the equation for which it is possible to describe explicitly all the solutions of the problem in terms of Morse graphs on the manifold. In particular, this proves that the $A_\infty$ structure of the zero section of the cotangent bundle is equivalent to the Morse $A_\infty$ structure of the base manifold.
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Obstructions to smoothing orbicurves and Orbifold Hecke algebras
Under mild assumptions the orbifold Hecke algebra of [X/G] is isomorphic to the degree-0 cohomology of the A∞-endomorphism algebra of a regular cotangent fiber in the bulk-deformed wrapped Fukaya category of T*[X/G].
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