Research on intersection of a pair of Lagrangian submanifolds via Floer theory

Arnold-Givental猜想指出了拉格朗日子流形L的交点数（即辛流形M的反辛对合的不动点集）与它的imageΦ(L)与hamilton量diffeomorphismΦof M的交点集的交点数大于等于L的Z_2-Betti数之和。在紧型不可约厄密对称空间M的情况下，给出了广义Arnold-Givental猜想。

The Arnold-Givental conjecture states that the intersection number of Lagrangian submanifold L, which is the fixed point set of an anti-symplectic involution of a symplectic manifold M, and its imageΦ(L) by Hamiltonian diffeomorphismΦof M is greater than or equal to the sum of Z_2-Betti numbers of L. We tried to extend the conjecture to the case of a pair of Lagrangian submanifolds. As a result, we could formulate the generalized Arnold-Givental conjecture and prove it for the case of an irreducible Hermitian symmetric space M of compact type.