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Topological recursion associates to a spectral curve, a sequence ofmeromorphic differential forms. A tangent space to the "moduli space" ofspectral curves (its space of deformations) is locally described by meromorphic1-forms, and we use form-cycle duality to re-express it in terms of cycles(generalized cycles). This formulation allows to express the ABCD tensors ofQuantum Airy Structures acting on the vector space of cycles, in an intrinsicspectral-curve geometric way.

Topological Recursion, Airy structures in the space of cycles