Given a three-manifold with b_1=1 and a nontorsion spin^c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodic pro-spectra. Various functors applied to these invariants give different flavors of Seiberg-Witten Floer homology. We also construct stable homotopy versions of the relative Seiberg-Witten invariants for certain four-manifolds with boundary.
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Kronheimer et al. (2002) studied this question.
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