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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
DOI: https://doi.org/10.1090/S0273-0979-96-00625-8
MathSciNet review: 1339810
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  • 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 $\mathbf{Z}^{n}$-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 $4$-manifolds with $b_{+}=1$, 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 $4$-manifolds, Proc. Int. Congress Mathematicians, Kyoto 1990, 1990, pp. (529-539), MR 93d:57066.
  • KL D. Kotschick and P.Lisca, Instanton invariants of $\mathbf{C}\mathbf{P}^{2}$ 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 $N=2$ supersymmetric QCD, Nucl. Phys. B 431 (1994), 581-640, CMP 95:05.
  • St A. Stipsicz, Donaldson invariants of certain symplectic $4$-manifolds, Crelles Journal (To appear).
  • Su D. Sullivan, Exterior $d$, 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: https://doi.org/10.1090/S0273-0979-96-00625-8
Received by editor(s): May 15, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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