SW ⇒ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves

Taubes, Clifford

doi:10.1090/S0894-0347-96-00211-1

SW $\Rightarrow$ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves
HTML articles powered by AMS MathViewer

by Clifford H. Taubes PDF

J. Amer. Math. Soc. 9 (1996), 845-918 Request permission

References

Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
Thierry Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 252, Springer-Verlag, New York, 1982. MR 681859, DOI 10.1007/978-1-4612-5734-9
Sheldon Xu-Dong Chang, Two-dimensional area minimizing integral currents are classical minimal surfaces, J. Amer. Math. Soc. 1 (1988), no. 4, 699–778. MR 946554, DOI 10.1090/S0894-0347-1988-0946554-0
S. K. Donaldson, Lectures at MIT, September 1994.
Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
Herbert Federer and Wendell H. Fleming, Normal and integral currents, Ann. of Math. (2) 72 (1960), 458–520. MR 123260, DOI 10.2307/1970227
R. Fintushel and R. Stern, Immersed spheres in $4$-manifolds and the immersed Thom Conjecture, preprint, 1995.
Daniel S. Freed and Karen K. Uhlenbeck, Instantons and four-manifolds, Mathematical Sciences Research Institute Publications, vol. 1, Springer-Verlag, New York, 1984. MR 757358, DOI 10.1007/978-1-4684-0258-2
M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718, DOI 10.1007/BF01388806
Arthur Jaffe and Clifford Taubes, Vortices and monopoles, Progress in Physics, vol. 2, Birkhäuser, Boston, Mass., 1980. Structure of static gauge theories. MR 614447
James R. King, The currents defined by analytic varieties, Acta Math. 127 (1971), no. 3-4, 185–220. MR 393550, DOI 10.1007/BF02392053
P. B. Kronheimer and T. S. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994), no. 6, 797–808. MR 1306022, DOI 10.4310/MRL.1994.v1.n6.a14
P. B. Kronheimer and T. S. Mrowka, Recurrence relations and asymptotics for four-manifold invariants, Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 2, 215–221. MR 1246469, DOI 10.1090/S0273-0979-1994-00492-6
H. Blaine Lawson Jr., Minimal varieties in real and complex geometry, Séminaire de Mathématiques Supérieures, No. 57 (Été 1973), Les Presses de l’Université de Montréal, Montreal, Que., 1974. MR 0474148
D. McDuff and D. Salamon, $J$-Holomorphic Curves and Quantum Cohomology, preprint.
J. W. Morgan, Z. Szabó, and C. H. Taubes, A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture, preprint, 1995.
Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511, DOI 10.1007/978-3-540-69952-1
T. S. Mrowka, Lectures at Harvard University, Spring, 1995.
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.
Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), no. 1, 1–24. MR 604040, DOI 10.2307/1971131
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in $N=2$ supersymmetric Yang-Mills theory, Nuclear Phys. B 426 (1994), no. 1, 19–52. MR 1293681, DOI 10.1016/0550-3213(94)90124-4
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in $N=2$ supersymmetric QCD, Nuclear Phys. B 431 (1994), no. 3, 484–550. MR 1306869, DOI 10.1016/0550-3213(94)90214-3
S. Smale, An infinite dimensional version of Sard’s theorem, Amer. J. Math. 87 (1965), 861–866. MR 185604, DOI 10.2307/2373250
Wilhelm Stoll, The growth of the area of a transcendental analytic set. I, II, Math. Ann. 156 (1964), 144–170. MR 166393, DOI 10.1007/BF01359928
Clifford Henry Taubes, The Seiberg-Witten and Gromov invariants, Math. Res. Lett. 2 (1995), no. 2, 221–238. MR 1324704, DOI 10.4310/MRL.1995.v2.n2.a10
Clifford Henry Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994), no. 6, 809–822. MR 1306023, DOI 10.4310/MRL.1994.v1.n6.a15
Clifford Henry Taubes, On the equivalence of the first and second order equations for gauge theories, Comm. Math. Phys. 75 (1980), no. 3, 207–227. MR 581946, DOI 10.1007/BF01212709
Clifford Henry Taubes, Arbitrary $N$-vortex solutions to the first order Ginzburg-Landau equations, Comm. Math. Phys. 72 (1980), no. 3, 277–292. MR 573986, DOI 10.1007/BF01197552
Clifford Henry Taubes, More constraints on symplectic forms from Seiberg-Witten invariants, Math. Res. Lett. 2 (1995), no. 1, 9–13. MR 1312973, DOI 10.4310/MRL.1995.v2.n1.a2
E. Witten, Monopoles and $4$-manifolds, Math. Res. Letters 1 (1994), 769–796.
Rugang Ye, Gromov’s compactness theorem for pseudo holomorphic curves, Trans. Amer. Math. Soc. 342 (1994), no. 2, 671–694. MR 1176088, DOI 10.1090/S0002-9947-1994-1176088-1