SEIBERG-WITTEN MONOPOLES IN 3 DIMENSIONS

Dimensional reduction of the Seiberg-Witten equations leads to the equ ations of motion of a U(1)Chern-Simons theory coupled to a massless sp inorial field. A topological quantum field theory is constructed for t he moduli space of gauge equivalence classes of solutions of these equ ations. The Euler characteristic of the moduli space is obtained as th e partition function which yields an analogue of Casson's invariant. A mathematically rigorous definition of the invariant is developed for homology spheres using the theory of spectral Row of self-adjoint Fred holm operators.