Abstract

We derive a cut-and-paste surgery formula of Seiberg–Witten invariants for negative definite plumbed rational homology 3-spheres. It is similar to (and motivated by) Okuma's recursion formula [Trans. Amer. Math. Soc.], 4.5, targeting analytic invariants of splice-quotient singularities. Combining the two formulas automatically provides a proof of the equivariant version [Némethi, Line bundles associated with normal surface singularities, World Sci. Publ., 2007], 5.2(b), of the Seiberg–Witten invariant conjecture [Némethi and Nicolaescu, Geom. Topol. 6: 269–328, 2002] for these singularities.