Associates to a relatively spin Lagrangian an open-closed DM field theory that extends the Fukaya A_infinity algebra to arbitrary genus and boundary components, unique up to homotopy.
MR 4179586 28 [Fuk10] Kenji Fukaya,Cyclic symmetry and adic convergence in Lagrangian Floer theory, Kyoto J
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Proves that injectivity of the quantum-to-Hochschild map implies split generation by the given Lagrangians and isomorphism of Fukaya (co)homology with quantum cohomology, extending the exact case.
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Open-closed Deligne-Mumford field theories: construction
Associates to a relatively spin Lagrangian an open-closed DM field theory that extends the Fukaya A_infinity algebra to arbitrary genus and boundary components, unique up to homotopy.
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Quantum cohomology and split generation in Lagrangian Floer theory
Proves that injectivity of the quantum-to-Hochschild map implies split generation by the given Lagrangians and isomorphism of Fukaya (co)homology with quantum cohomology, extending the exact case.