Every interior toric fiber in FOOO's resolved toric model of S^2×S^2 is either Hamiltonian isotopic to a standard toric fiber away from the diagonal, or not even isotopic to a product torus on the diagonal.
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On Lagrangian Tori in $S^2\times S^2$
Every interior toric fiber in FOOO's resolved toric model of S^2×S^2 is either Hamiltonian isotopic to a standard toric fiber away from the diagonal, or not even isotopic to a product torus on the diagonal.