|
SW 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
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
References |
Similar articles |
Additional information
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
-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,
-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
-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
supersymmetric Yang-Mills theory, Nucl. Phys. B426 (1994), 19--52. MR 95m:81202a; MR 95m:81202b - [SW2]
- ------, Monopoles, duality and chiral symmetry breaking in
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
-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
-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
Similar Articles:
Retrieve articles in Journal of the American Mathematical Society
with MSC
(1991):
53C07, 53C15
Retrieve articles in all Journals with MSC
(1991):
53C07, 53C15
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
|