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TITLE Anti-symplectic involutions for Lagrangian spheres in a symplectic quadric surface Kim, Joontae,Kim, Joontae online ready in Bulletin of the London Mathematical Society, https://doi.org/10.1112/blms.12533 We show that the space of anti-symplectic involutions of a monotone $S2\times S2$ whose fixed point set is a Lagrangian sphere is connected. This follows from a stronger result, namely that any two anti-symplectic involutions in that space are Hamiltonian isotopic.