Abstract
Given a closed oriented surface \Sigma of genus greater than 0, we construct a map \mathcal{F} from the wrapped higher-dimensional Heegaard Floer homology of the cotangent fibers of T^{*}\Sigma to the Hecke algebra associated to \Sigma and show that \mathcal{F} is an isomorphism of algebras. We also establish analogous results for punctured surfaces.
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