Surgery formulae for the Seiberg–Witten invariant of plumbed 3-manifolds

Assume that [Formula: see text] is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph [Formula: see text] . We consider the combinatorial multivariable Poincaré series associated with [Formula: see text] and its counting functions, which encode rich topological information. Using the ‘periodic constant’ of the series (with reduced variables associated with an arbitrary subset [Formula: see text] of the set of vertices) we prove surgery formulae for the normalized Seiberg–Witten invariants: the periodic constant associated with [Formula: see text] appears as the difference of the Seiberg–Witten invariants of [Formula: see text] and [Formula: see text] for any [Formula: see text] .