Abstract
The goal of this paper is to give a new proof of a theorem of Meng and
Taubes that identifies the Seiberg-Witten invariants of 3-manifolds with
Milnor torsion. The point of view here will be that of topological quantum
field theory. In particular, we relate the Seiberg-Witten equations on a
3-manifold with the Abelian vortex equations on a Riemann surface. These
techniques also give a new proof of the surgery formula for the Casson
invariant, interpreted as an invariant of a homology S^2 x S^1.
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