Lagrangian Floer homology of the Clifford torus and real projective space in odd dimensions

The Floer homology of the pair (RP 2n-1 , T 2n-1 ) in CP 2n-1 is calculated and is shown to have dimension 2 n , both with Z 2 and Z2 coefficients. In particular, this implies that RP 2n-1 and T 2n-1 must always intersect in at least 2 n points under Hamiltonian isotopy (if the intersection is transverse).