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

Tamás László; János Nagy; András Némethi

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arXiv · 1702.06692

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

Tamás László·János Nagy·András Némethi

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Abstract

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 $\mathcal{T}$.

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BibTeX RIS

Tamás László, János Nagy, András Némethi. 2017-02-22. Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds. https://arxiv.org/abs/1702.06692

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