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Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds
- Publication Year :
- 2017
-
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 $\mathcal{T}$.<br />Comment: 24 pages
- Subjects :
- Mathematics - Geometric Topology
Mathematics - Algebraic Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1702.06692
- Document Type :
- Working Paper