The BRST operator of quantum symmetries: The quantum analogs of Donaldson invariants

We construct the BRST operator of quantum symmetries and show that the nilpotency of this operator can either be derived from the Hopf axiom structure of the quantum group symmetries or from the Jacobi identity of their quantum Lie algebra. We extend this BRST operator to the topological transformations and we investigate the propel-ties of invariant polynomials of curvatures from which we derive the descent equations for Donaldson invariants. (C) 1997 American Institute of Physics.