(Note: abstract and paper revised since preprint version.)
Dimensional reduction of the Seiberg-Witten equations leads to the equations of motion of a U(1) Chern-Simons theory coupled to a massless spinorial field. A topological quantum field theory is constructed for the moduli space of gauge equivalence classes of solutions of these equations. The Euler characteristic of the moduli space is obtained as the 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 Fredholm operators.
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