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The Seiberg-Witten equations and 4-manifold topology
Author:
S. K. Donaldson
Journal:
Bull. Amer. Math. Soc. 33 (1996), 45-70
MSC (1991):
Primary 58-02
MathSciNet review:
1339810
Full-text PDF
References |
Similar Articles |
Additional Information
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A. Stipsicz, Donaldson invariants of certain symplectic
-manifolds, Crelles Journal (To appear).
- Su
D. Sullivan, Exterior
, the local index and smoothability, IHES preprint (1995).
- T1
C. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1 (1994), 809-822, CMP 95:05.
- T2
C. Taubes, More constraints on symplectic forms from Seiberg-Witten equations, Math. Res. Letters 2 (1995), 9-14, CMP 95:07.
- T3
C. Taubes, The Seiberg-Witten and the Gromov invariants, Harvard Preprint (1995).
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Michael
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- VW
C. Vafa and E. Witten, A strong coupling test of S-duality, Nucl. Phys. B (To appear), CMP 95:04.
- W1
Edward
Witten, Topological quantum field theory, Comm. Math. Phys.
117 (1988), no. 3, 353–386. MR 953828
(89m:57037)
- W2
E. Witten, Supersymmetric Yang-Mills theory on a four-manifold, J. Math. Phys. 35 (1994), CMP 95:01.
- W3
E. Witten, Monopoles and 4-manifolds, Math. Res. Letters 1 (1994), 769-796, CMP 95:05.
- AJ
- M. F. Atiyah and L. C. Jeffrey, Topological Lagrangians and cohomology, Jour. Geometry and Physics 7 (1990), 119--136, MR 92f:58025.
- A
- D. Austin, Equivariant Floer Theory for binary polyhedral spaces, Preprint.
- AB
- D. Austin and P. Braam, Equivariant Floer cohomology, Topology (To appear).
- BDGW
- S. Bradlow, G. Daskalopoulos, O. Garcia-Prada, R. Wentworth, Stable augmented bundles over Riemann surfaces, Vector bundles in algebraic geometry (Ed. Hitchin, Newstead, Oxbury), Cambridge UP, 1995.
- D1
- S. Donaldson, Connections, cohomology and the intersection forms of four manifolds, Jour. Differential Geometry 24 (1986), 275--341, MR 88g:57033.
- D2
- S. Donaldson, Irrationality and the h-cobordism conjecture, Jour. Differential Geometry 26 (1987), 141-168, MR 88j:57035.
- D3
- S. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), 257-315, MR 92a:57035.
- D4
- S. Donaldson, Yang-Mills invariants of four-manifolds, Geometry of low-dimensional manifolds, Vol I (Ed. Donaldson and Thomas), Cambridge UP, 1990.
- DK
- S. Donaldson and P. Kronheimer, The geometry of four-manifolds, Oxford UP, 1990, MR 92a:57036.
- DS
- S. Donaldson and D. Sullivan, Quasiconformal four-manifolds, Acta Math. 163 (1989), 181-252, MR 91d:57012.
- E
- N. Elkies, A characterisation of the
-lattice, Math. Res. Letters (To appear).
- FS
- R. Fintushel and R. Stern, The blowup formula for Donaldson invariants, Preprint (1994).
- FM
- R. Friedman and J. Morgan, Algebraic surfaces and four-manifolds: some conjectures and speculations, Bull. Amer. Math. Soc. 18 (1988), 1-19, MR 89g:57046.
- FQ
- R. Friedman and Z. Qin, The smooth invariance of the Kodaira dimension of a complex surface, Math. Res. Letters 1 (1994), 369-376, CMP 95:04.
- Go
- R. Gompf, A new construction of symplectic manifolds, Preprint (1994).
- Got
- L. Gottsche, Modular forms and Donaldson invariants for
-manifolds with , Preprint (1995).
- Gr
- M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Inventiones Math. 82 (1985), 305-347, MR 87j:53053.
- GL
- M. Gromov and H. Lawson, The classification of simply-connected manifolds of positive scalar curvature, Ann of Math (2) 111 (1980), 423-434, MR 81h:53036.
- H
- N. Hitchin, The self-duality equations on a Riemann surface, Proc. Lond. Math. Soc. 55 (1987), 59-126, MR 89a:32021.
- JT
- A. Jaffe and C. Taubes, Vortices and monopoles, Birkhauser, 1980, MR 82m:81051.
- K
- P. Kronheimer, Embedded surfaces in
-manifolds, Proc. Int. Congress Mathematicians, Kyoto 1990, 1990, pp. (529-539), MR 93d:57066.
- KL
- D. Kotschick and P.Lisca, Instanton invariants of
via topology, preprint.
- KM1
- P. Kronheimer and T. Mrowka, Gauge theory for embedded surfaces, Topology 32 (1993), 773-826, MR 94k:57048.
- KM2
- P. Kronheimer and T. Mrowka, Recurrence relations and asymptotics for four-manifold invariants, Bull. Amer. Math. Soc. 30 (1994), 215--221, MR 94k:57046.
- KM3
- P. Kronheimer and T. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Letters 1 (1994), 797-808, CMP 95:05.
- L
- C. LeBrun, Einstein metrics and Mostow rigidity, Math. Res. Letters 2 (1995), 1-8, CMP 95:07.
- M
- M. Manetti, On some components of moduli spaces of surfaces of general type, Compositio Math. 92 (1994), 285-297, CMP 94:15.
- MST
- J. Morgan, Z. Szabo and C. Taubes, The generalised Thom conjecture, In preparation.
- PT
- V. Pidstragach and A. Tyurin, Invariants of the smooth structure of an algebraic surface arising from the Dirac operator (English translation), Russian Math. Surveys (1994).
- S
- N. Seiberg, Phys.Lett. B 318 (1993), 469, MR 93m:14036.
- SW
- N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in
supersymmetric QCD, Nucl. Phys. B 431 (1994), 581-640, CMP 95:05.
- St
- A. Stipsicz, Donaldson invariants of certain symplectic
-manifolds, Crelles Journal (To appear).
- Su
- D. Sullivan, Exterior
, the local index and smoothability, IHES preprint (1995).
- T1
- C. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1 (1994), 809-822, CMP 95:05.
- T2
- C. Taubes, More constraints on symplectic forms from Seiberg-Witten equations, Math. Res. Letters 2 (1995), 9-14, CMP 95:07.
- T3
- C. Taubes, The Seiberg-Witten and the Gromov invariants, Harvard Preprint (1995).
- Th
- M. Thaddeus, Stable pairs, linear systems and the Verlinde formula, Inventiones Math. 117 (1994), 317-353, MR 95e:14006.
- VW
- C. Vafa and E. Witten, A strong coupling test of S-duality, Nucl. Phys. B (To appear), CMP 95:04.
- W1
- E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988), 353-386, MR 89m:57037.
- W2
- E. Witten, Supersymmetric Yang-Mills theory on a four-manifold, J. Math. Phys. 35 (1994), CMP 95:01.
- W3
- E. Witten, Monopoles and 4-manifolds, Math. Res. Letters 1 (1994), 769-796, CMP 95:05.
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Additional Information
S. K. Donaldson
Affiliation:
The Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford OX1 3LB, England
Email:
donaldson@vax.ox.ac.uk
DOI:
http://dx.doi.org/10.1090/S0273-0979-96-00625-8
PII:
S 0273-0979(96)00625-8
Received by editor(s):
May 15, 1995
Article copyright:
© Copyright 1996 American Mathematical Society
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