Anti‐symplectic involutions for Lagrangian spheres in a symplectic quadric surface

We show that the space of anti-symplectic involutions of a monotone $S^2\times S^2$ whose fixed points 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.
8 pages, 1 figure