Conjectures on counting associative 3-folds in $G_2$-manifolds by Joyce, D

“…Several areas of Symplectic Geometry – Gromov–Witten theory, Quantum Cohomology, Lagrangian Floer cohomology, Fukaya categories – are built using ‘counts’ of moduli spaces of J-holomorphic curves in Y , but give an answer depending only on the symplectic manifold (Y,ω), not on the (almost) complex structure J. …”