We define quantum exterior product ∧h and quantum exterior differential dh on Poisson manifolds, of which symplectic manifolds are an important class of examples. Quantum de Rham cohomology is defined as the cohomology of dh. We also define quantum Dolbeault cohomology. Quantum hard Lefschetz theorem is proved. We also define a version of quantum integral, and prove the quantum Stokes theorem. ...
