Abstract
Associativity of the quantum product ensures flatness of the Dubrovin connection and is the basis for Hodge-theoretic mirror symmetry of Calabi-Yau threefolds. We use ring and module structure on cohomology pertaining to a Lagrangian submanifold to define an extension of the A-model Variation of mixed Hodge structure that matches the predictions from extended mirror symmetry. Our construction makes contact with axioms for open Gromov-Witten theory recently proposed by Solomon-Tukachinsky.
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