Let (X, ω) be a compact symplectic manifold, L be a Lagrangian submanifold and V be a codimension 2 symplectic submanifold of X, we consider the pseudoholomorphic maps from a Riemann surface with boundary (Σ, ∂Σ) to the pair (X, L) satisfying Lagrangian boundary conditions and intersecting V. We study the stable moduli space of such open pseudoholomorphic maps involving the intersection data. Assume that L ∩ V = ∅ and there exists an anti-symplectic involution φ on X such that L is the fixed point set of φ and V is φ-anti-invariant. Then we define the so-called “relatively open ” invariants for the tuple (X, ω, V, φ) if L is orientable and dimX ≤ 6. If L is nonorientable, we define such invariants under the condition that dimX ≤ 4 and some additional restrictions on the number of marked points on each boundary component of the domain
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