Assume that $M(\mathcal{ T})$ is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph $\mathcal{ T}$. We consider the combinatorial multivariable Poincar\'e series associated with $\mathcal{ T}$ and its counting functions, which encode rich topological information. Using the `periodic constant' of the series (with reduced variables) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant appears as the difference of the Seiberg-Witten invariants associated with $M(\mathcal{ T})$ and $M(\mathcal{ T}\setminus\mathcal{ I})$, where $\mathcal{ I}$ is an arbitrary subset of the set of vertices of $\mathcal{ T}$.
Categories: math.GT math.AG