Non-normal affine monoids, modules and Poincaré series of plumbed 3-manifolds

Abstract

We construct a non-normal affine monoid together with its modules associated with a negative definite plumbed 3-manifold M. In terms of their structure, we describe the $H_1(M,\mathbb{Z})$-equivariant parts of the topological Poincaré series. In particular, we give combinatorial formulas for the Seiberg–Witten invariants of M and for polynomial generalizations defined in [17].