Topological Recursion, Airy structures in the space of cycles

Topological recursion associates to a spectral curve, a sequence of meromorphic differential forms. A tangent space to the moduli space of spectral curves (its space of deformations) is locally described by meromorphic 1-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 of Quantum Airy Structures acting on the vector space of cycles, in an intrinsic spectral-curve geometric way.