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SW $\Rightarrow $ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves

Author(s): Clifford H. Taubes
Journal: J. Amer. Math. Soc. 9 (1996), 845-918.
MSC (1991): Primary 53C07, 53C15
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References:

[Ar]
N. Aronszajn, A unique continuation theorem for elliptic differential equations or inequalities of the second order, J. Math. Pures Appl. 36 (1957), 235-249. MR 19:1056c

[Au]
T. Aubin, Nonlinear Analysis on Manifolds, Monge-Ampere Equations, Springer-Verlag, New York, 1982. MR 85j:58002

[Ch]
S. Chang, Two dimensional area minimizing integral currents are classical minimal surfaces, JAMS 1 (1988), 699--778. MR 89i:49028

[Do]
S. K. Donaldson, Lectures at MIT, September 1994.

[DN]
A. Douglis and L. Nirenberg, Interior estimates for elliptic systems of partial differential equations, Comm. Pure Appl. Math. 8 (1955), 503--538. MR 17:743b

[Fe]
H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969. MR 41:1976

[FF]
H. Federer and W. Fleming, Normal and integral currents, Ann. of Math. 72 (1960), 458--520. MR 23:A588

[FS]
R. Fintushel and R. Stern, Immersed spheres in $4$-manifolds and the immersed Thom Conjecture, preprint, 1995.

[FU]
D. Freed and K. K. Uhlenbeck, Instantons and Four Manifolds, Springer-Verlag, New York, 1984. MR 86c:57031

[Gr]
M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307--347. MR 87j:53053

[JT]
A. Jaffe and C. H. Taubes, Vortices and Monopoles, Birkhäuser, Boston, 1980. MR 82m:81051

[Ki]
J. R. King, The currents defined by analytic varieties, Acta Math. 127 (1971), 185--220. MR 52:14359

[KM1]
P. B. Kronheimer and T. S. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Letters 1 (1994), 797--808. MR 96a:57073

[KM2]
------, Recurrence relations and asymptotics for four-manifold invariants, Bull. Amer. Math. Soc. 30 (1994), 215--221. MR 94k:57046

[La]
H. B. Lawson, Minimal Varieties in Real and Complex Geometry, Sem. Math. Sup. Vol. 57, Presses Université de Montreal, 1974. MR 57:13798

[MS]
D. McDuff and D. Salamon, $J$-Holomorphic Curves and Quantum Cohomology, preprint.

[MST]
J. W. Morgan, Z. Szabó, and C. H. Taubes, A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture, preprint, 1995.

[Mo]
C. B. Morrey, Multiple integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966. MR 34:2380

[Mr]
T. S. Mrowka, Lectures at Harvard University, Spring, 1995.

[Rua]
Y. Ruan, Symplectic topology and complex surfaces, in Geometry and Topology on Complex Manifolds, T. Mabuchi, J. Noguchi, T. Ochial, eds., World Scientific Publications, Singapore, 1994.

[Rut]
H. Rutishauser, Uber die Folgen und Scharen von analytishen und meromorphen Funktionen mehrerer Variabeln, sowie von analytishen Abbildungen, Acta Math. 83 (1950), 249--325. MR 12:90f

[SU]
J. Sacks and K. K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. 113 (1981), 1--24. MR 82f:58035

[SW1]
N. Seiberg and E. Witten, Electro-magnetic duality, monopole condensation and confinement in $N=2$ supersymmetric Yang-Mills theory, Nucl. Phys. B426 (1994), 19--52. MR 95m:81202a; MR 95m:81202b

[SW2]
------, Monopoles, duality and chiral symmetry breaking in $N=2$ supersymmetric QCD, Nucl. Phys. B431 (1994), 485--550. MR 95m:81203

[SS]
S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861--866. MR 32:3067

[St]
W. Stoll, The growth of the area of a trancendental analytic set. I, Math. Ann. 156 (1964), 47--78. MR 29:3670

[T1]
C. H. Taubes, The Seiberg-Witten and the Gromov invariants, Math. Res. Letters 2 (1995), 221--238. MR 96a:57076

[T2]
------, The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1 (1995), 809--822. MR 95j:57039

[T3]
------, On the equivalence of first and second order equations for gauge theories, Commun. Math. Phys. 75 (1980), 207--227. MR 83b:81098

[T4]
------, Arbitrary $n$-vortex solutions to the first order Ginzburg-Landau equations, Commun. Math. Phys. 72 (1980), 277--292. MR 83c:81124

[T5]
------, More constraints on symplectic manifolds from the Seiberg-Witten invariants, Math. Res. Letters 2 (1995), 9--13. MR 96a:57075

[W]
E. Witten, Monopoles and $4$-manifolds, Math. Res. Letters 1 (1994), 769--796. CMP 95:05

[Ye]
R. Ye, Gromov's compactness theorem for pseudo-holomorphic curves, Trans. Amer. Math. Soc. 342 (1994), 671--694. MR 94f:58030


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Additional Information:

Clifford H. Taubes
Affiliation: Department of Mathematics, Harvard university, Cambridge, Massachusetts 02138
Email: chtaubes@math.harvard.edu

DOI: 10.1090/S0894-0347-96-00211-1
PII: S 0894-0347(96)00211-1
Received by editor(s): June 26, 1995
Received by editor(s) in revised form: August 7, 1995
Additional Notes: The author is supported in part by the National Science Foundation
Copyright of article: Copyright 1996, American Mathematical Society


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