Point-like bounding chains in open Gromov–Witten theory

We present a solution to the problem of defining genus zero open Gromov–Witten invariants with boundary constraints for Lagrangian submanifold arbitrary dimension. Previously, such were known only in dimensions 2 and 3 from work Welschinger. Our approach does not require be fixed by an anti-symplectic involution, but can use if present, obtain stronger results. Also, non-trivial are defined broader classes interior submanifolds than previously possible even presence involution. The specialize Welschinger, Fukaya, Georgieva many instances. main obstacle dimension is bubbling J-holomorphic disks. Unlike low or constraints, disk bubbles do cancel pairs involution symmetry. Rather, we technique bounding chains introduced Fukaya–Oh–Ohta–Ono’s on Floer theory bubbling. At same time independently, gauge equivalence play role place cohomology that usually serve as theory. A crucial step our construction identify canonical up family “point-like” chains, which point considered