Quantum hyperplane section theorem for homogeneous spaces

We formulated a mirror-free approach to the mirror conjecture, namely, quantum hyperplane section conjecture, and proved it in the case of nonnegative complete intersections in homogeneous manifolds. For the proof we followed the scheme of Givental’s proof of a mirror theorem for toric complete intersections. Furthermore, we observed that the conjecture is true also for any projective manifold. 1.