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

Tamás László; Zsolt Szilágyi

doi:10.1007/s10474-017-0726-2

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arXiv · 1612.07537

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

Tamás László·Zsolt Szilágyi

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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 a previous paper of the authors.

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Tamás László, Zsolt Szilágyi. 2016-12-22. Non-normal affine monoids, modules and Poincaré series of plumbed 3-manifolds. https://doi.org/10.1007/s10474-017-0726-2

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