Seiberg–Witten Invariant of the Universal Abelian Cover of $${S_{-p/q}^{3}(K)}$$

Bodnár, József; Némethi, András

doi:10.1007/978-3-319-28829-1_9

Cited by 7 publications

(5 citation statements)

References 33 publications

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“…The schematic picture of the plumbing graph

normalΓ

of the oriented 3–manifold

M = S_{- p / q}^{3} false(K false)

has the form as shown in Figure (see ), where the dash‐lines represent strings of vertices.…”

Section: Comparison and Examples For P And P+mentioning

confidence: 99%

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Némethi's division algorithm for zeta-functions of plumbed 3-manifolds

Tamás

Szilágyi

2018

Bull. London Math. Soc.

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A polynomial counterpart of the Seiberg–Witten invariant associated with a negative definite plumbing 3‐manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta‐function defined by the combinatorics of the manifold. In this article we give an algorithm, based on multivariable Euclidean division of the zeta‐function, for the explicit calculation of the polynomial, in particular for the Seiberg–Witten invariant.

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“…The schematic picture of the plumbing graph

normalΓ

of the oriented 3–manifold

M = S_{- p / q}^{3} false(K false)

has the form as shown in Figure (see ), where the dash‐lines represent strings of vertices.…”

Section: Comparison and Examples For P And P+mentioning

confidence: 99%

“…It is also known that the homology group

H = L^{'} / L ≃ {double-struckZ}_{p}

is the cyclic group of order

p

, generated by

[E_{+ s}^{*}]

(for a complete proof see [, Lemma 6]).…”

Section: Comparison and Examples For P And P+mentioning

confidence: 99%

Némethi's division algorithm for zeta-functions of plumbed 3-manifolds

Tamás

Szilágyi

2018

Bull. London Math. Soc.

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“…For several properties of the lattice cohomology and applications in singularity theory see [38,39,40,44,45]. For its connection with the classification of projective rational plane cuspidal curves (via superisolated surface singularities) see [39,9,10,11,12,13]. It provides sharp topological bounds for certain sheaf cohomologies (e.g.…”

Section: Introductionmentioning

confidence: 99%

Analytic lattice cohomology of surface singularities

Ágoston,

Némethi

2021

Preprint

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We construct the analytic lattice cohomology associated with the analytic type of any complex normal surface singularity. It is the categorification of the geometric genus of the germ, whenever the link is a rational homology sphere.It is the analytic analogue of the topological lattice cohomology, associated with the link of the germ whenever it is a rational homology sphere. This topological lattice cohomology is the categorification of the Seiberg-Witten invariant, and conjecturally it is isomorphic with the Heegaard Floer cohomology.We compare the two lattice cohomologies: in some simple cases they coincide, but in general, the analytic cohomology is sensitive to the analytic structure. We expect a deep connection with deformation theory. We provide several basic properties and key examples, and we formulate several conjectures and problems. This is the initial article of a series, in which we develop the analytic lattice cohomology of singularities.X → X (and in some of the cases below we need to assume that the link is a rational homology sphere).

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“…For several properties and application in singularity theory see [25,26,27,30,31]. For its connection with the classification projective rational plane cuspidal curves (via superisolated surface singularities) see [26,6,7,8,9,10]. It provides sharp topological bounds for certain sheaf cohomologies (e.g.…”

Section: Introductionmentioning

confidence: 99%

Analytic lattice cohomology of surface singularities, II (the equivariant case)

Ágoston,

Némethi

2021

Preprint

Self Cite

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We construct the equivariant analytic lattice cohomology associated with the analytic type of a complex normal surface singularity whenever the link is a rational homology sphere. It is the categorification of the equivariant geometric genus of the germ. This is the analytic analogue of the topological lattice cohomology, associated with the link of the germ, and indexed by the spin c -structures of the link (which is a categorification of the Seiberg-Witten invariant and conjecturally it is isomorphic with the Heegaard Floer cohomology).

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Seiberg–Witten Invariant of the Universal Abelian Cover of $${S_{-p/q}^{3}(K)}$$

Cited by 7 publications

References 33 publications

Némethi's division algorithm for zeta-functions of plumbed 3-manifolds

Némethi's division algorithm for zeta-functions of plumbed 3-manifolds

Analytic lattice cohomology of surface singularities

Analytic lattice cohomology of surface singularities, II (the equivariant case)

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