Arnold–Givental conjecture
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The Arnold–Givental conjecture, named after Vladimir Arnold and Alexander Givental, is a statement on Lagrangian submanifolds. It gives a lower bound in terms of the Betti numbers of a Lagrangian submanifold L on the number of intersection points of L with another Lagrangian submanifold which is obtained from L by Hamiltonian isotopy, and which intersects L transversally.