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Quantum periods - I. Semi-infinite variations of Hodge structures

S. Barannikov
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Abstract

We introduce a generalization of variations of Hodge structures living over moduli spaces of non-commutative deformations of complex manifolds. Hodge structure associated with a point of such moduli space is an element of Sato type grassmanian of semi-infinite subspaces in H^*(X,C)[[h^{-1},h]]. Periods associated with such semi-infinite Hodge structures serve in order to extend mirror symmetry relations in dimensions greater then three.

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S. Barannikov. 2000-06-26. Quantum periods - I. Semi-infinite variations of Hodge structures. https://doi.org/10.1155/s1073792801000599

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