Seiberg-Witten and Gromov invariants for symplectic 4-manifolds

By Clifford H. Taubes, R. Wentworth. 2005

145 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e4579c1c31b692e9377ae1ac58d1e9d671fbc6b4

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Citations in the corpus

Infinitely many monotone Lagrangian tori in del Pezzo surfaces (2016, methodology): “Proof Indeed, given an ATBD of triangular shape, its Euler characteristic is given by n1+n2+n3 [31, Section 8.1], and the total space isCP2#kCP2 for k = n1+n2+n3−3, orCP1×CP1 if n1+n2+n3 = 4 [23, Table 1].”
Symplectic Floer homology of area-preserving surface diffeomorphisms (2008, background): “This theory was created to be a candidate for a 3-dimensional version of Taubes’ “SW = Gr” result [Ta1] and is conjectured [HS1] to be isomorphic to the Seiberg-Witten Floer homology (SWFH) [KM] of Mφ in certain spinstructures when d < g−1.”
The Seiberg–Witten equations and the Weinstein conjecture (2006, background): “This said, note that a sequel to this article is planned to connect the story told here with the 4–dimensional story that is told in [26] (see Taubes [29]).”
Quantitative embedded contact homology (2010, methodology): “9 is not new and, as explained to me by Dusa McDuff, can also be deduced by applying Taubes’s “Seiberg-Witten = Gromov” theorem [20] to a symplectic blowup of CP (2).”
Embedded contact homology and Seiberg–Witten Floer cohomology II (2008, methodology): “Theorem 1 can be viewed as the 3-manifold analog of the equivalence proved in [T1], [ T2 ] between the Seiberg-Witten invariants of a compact symplectic manifold and certain of the Gromov invariants that are computed by counting its pseudoholomorphic curves.”
Symplectic embeddings from concave toric domains into convex ones (2014, background): “ class A, for generic !-compatible almost complex structure J, see for example [16, 14 x2] for details. A symplectic form !denes a spinc structure s !, and the \Seiberg-Witten = Gromov" theorem [32] states that there is an equivalence GrpAqSWpAq; (4.1) where SWpAqdenotes the Seiberg-Witten inva”
Taubes’s proof of the Weinstein conjecture in dimension three (2009, methodology): “rem is now: Theorem 7.1 (Taubes). Let Xbe a closed connected symplectic 4-manifold with b+ 2 (X) >1. Then for each s ∈ Spinc(X) we have SW(X,s) = Gr(X,ıω(s)). The proof of this theorem is given in [61]; for an introduction to it see [34], and for a discussion from a physics perspective see [74]. ”
The Gromov width of 4-dimensional tori (2011, background): “E/¤ 0 follows from Taubes’ work on the relation between Seiberg–Witten and Gromov invariants, according to which for any symplectic form ! on z X the class E is representable by an embedded sphere on which ! is non-degenerate; see [38; 39].”
Lagrangian matching invariants for fibred four-manifolds: I (2006, background): “The moduli space of solutions to these equations is a symmetric product of the surface; in the ‘adiabatic limit’ as the base of the fibration is expanded , solutions to the Seiberg‐ Witten equations approximate pseudo-holomorphic curves in the family of vortex moduli spaces [24, 31 ].”
Holomorphic disks and genus bounds (2003, unknown): “[38].”
Lecture Notes on Embedded Contact Homology (2013, background): “The starting point for the definition of ECH is Taubes’s “SW=Gr” theorem [55] asserting that the Seiberg-Witten invariants of a symplectic four-manifold agree with a “Gromov invariant” counting holomorphic curves.”
Regularity of area minimizing currents I: gradient Lp estimates (2013, unknown): “The interest in the regularity theory for this class of area minimizing two-dimensional currents has been generated by the seminal paper of Taubes [Tau00] on the equivalence between Gromov and Seiberg–Witten invariants, where it plays an important role.”
Six Lectures on Four 4-Manifolds (2006, background): “where e = tE. The assumption of simple type is true for all symplectic manifolds with b+ > 1 by a theorem of Taubes [ 56 ].”
Uniqueness of symplectic structures (2012, methodology): “∗Partially supported by the Swiss National Science Foundation Grant 200021-127136”