On the Quantum Homology of Real Lagrangians in Fano Toric Manifolds

Let R be the real Lagrangian in a toric symplectic manifold X, the fixed point set under complex conjugation. Assuming that X is Fano of minimal Chern number at least 2, we show that the Lagrangian quantum homology QH(R;Λ) of R over the ring $\Lambda =\mathbb{Z}_{2}[t,t^{-1}]$ is isomorphic to $H(R;\mathbb{Z}_{2})\otimes \Lambda$ as a module. Moreover, we prove that QH(R;Λ) is isomorphic as a ring to the quantum homology QH(X;Λ) of the ambient symplectic manifold.