# The Seiberg–Witten invariants of negative definite plumbed 3-manifolds

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 4, page 959-974
- ISSN: 1435-9855

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topNémethi, András. "The Seiberg–Witten invariants of negative definite plumbed 3-manifolds." Journal of the European Mathematical Society 013.4 (2011): 959-974. <http://eudml.org/doc/277720>.

@article{Némethi2011,

abstract = {Assume that $\Gamma $ is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold $M$ is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of $M$. The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph $\Gamma $, and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second formula realizes the Seiberg–Witten invariant as the normalized Euler characteristic of the lattice cohomology associated with $\Gamma $, supporting the conjectural connections between the Seiberg–Witten Floer homology, or the Heegaard–Floer homology, and the lattice cohomology.},

author = {Némethi, András},

journal = {Journal of the European Mathematical Society},

keywords = {normal surface singularities; resolutions of singularities; links of singularities; plumbed 3-manifolds; plumbing graphs; Seiberg–Witten invariants; surgery formulae; periodic constant; Hilbert polynomials; Seiberg–Witten Invariant Conjecture; zeta-function; lattice cohomology; Heegaard-Floer homology; normal surface singularities; links of singularities; Seiberg-Witten invariants; Hilbert polynomials; Heegaard-Floer homology},

language = {eng},

number = {4},

pages = {959-974},

publisher = {European Mathematical Society Publishing House},

title = {The Seiberg–Witten invariants of negative definite plumbed 3-manifolds},

url = {http://eudml.org/doc/277720},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Némethi, András

TI - The Seiberg–Witten invariants of negative definite plumbed 3-manifolds

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 4

SP - 959

EP - 974

AB - Assume that $\Gamma $ is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold $M$ is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of $M$. The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph $\Gamma $, and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second formula realizes the Seiberg–Witten invariant as the normalized Euler characteristic of the lattice cohomology associated with $\Gamma $, supporting the conjectural connections between the Seiberg–Witten Floer homology, or the Heegaard–Floer homology, and the lattice cohomology.

LA - eng

KW - normal surface singularities; resolutions of singularities; links of singularities; plumbed 3-manifolds; plumbing graphs; Seiberg–Witten invariants; surgery formulae; periodic constant; Hilbert polynomials; Seiberg–Witten Invariant Conjecture; zeta-function; lattice cohomology; Heegaard-Floer homology; normal surface singularities; links of singularities; Seiberg-Witten invariants; Hilbert polynomials; Heegaard-Floer homology

UR - http://eudml.org/doc/277720

ER -

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