Equivariant Lagrangian Floer theory and mirror symmetry
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In this thesis, we develop a Morse model for G-equivariant Lagrangian Floer theory and use it to study equivariant mirror symmetry from the perspective of SYZ. In the case of a semi-Fano toric manifold, we show that the T-equivariant SYZ mirror we obtain is the T-equivariant toric Landau-Ginzburg mirror of Givental. We also compute the equivariant disc potential of immersed SYZ fibers in toric Calabi-Yau manifolds and obtain interesting invariants. In dimension three, it is closely related to open Gromov-Witten invariants of Aganagic-Vafa branes.
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