NON-ABELIAN MONOPOLES ON 4-MANIFOLDS

We present a non-abelian generalization of Seiberg-Witten monopole equ ations and we analyze the associated moduli problem, which can be rega rded as a generalization of Donaldson theory. The moduli space of solu tions for SU(2) monopoles on Kahler manifolds is discussed. We also co nstruct, using the Mathai-Quillen formalism, the topological quantum f ield theory corresponding to the new moduli problem. This theory invol ves the coupling of topological Yang-Mills theory to topological matte r in four dimensions.