Establishes calculus structure on Hochschild invariants of open-closed homotopy algebras and shows the Getzler-Gauss-Manin connection is flat up to chain homotopy on the periodic cyclic chain complex.
Lagrangian Floer theory and mirror symmetry on compact toric manifolds
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abstract
In this paper we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We construct a natural isomorphism between the Frobenius manifold structures of the (big) quantum cohomology of the toric manifold and of Saito's theory of singularities of the potential function constructed in \cite{fooo09} via the Floer cohomology deformed by ambient cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop.
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math.QA 1years
2026 1verdicts
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Non-commutative calculus and Getzler-Gauss-Manin connections for Open-closed Homotopy Algebras
Establishes calculus structure on Hochschild invariants of open-closed homotopy algebras and shows the Getzler-Gauss-Manin connection is flat up to chain homotopy on the periodic cyclic chain complex.