Abstract
We consider a modified version of the Seiberg–Witten invariants for rational homology 3-spheres, obtained by adding to the original invariants a correction term which is a combination of η-invariants. We show that these modified invariants are topological invariants. We prove that an averaged version of these modified invariants equals the Casson–Walker invariant. In particular, this result proves an averaged version of a conjecture of Ozsvath and Szabo on the equivalence between their θ invariant and the Seiberg–Witten invariant of rational homology 3-spheres.
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