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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
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  • M. F. Atiyah and L. Jeffrey, Topological Lagrangians and cohomology, J. Geom. Phys. 7 (1990), no. 1, 119–136. MR 1094734, DOI
  • \key A \by D. Austin \pages\paper Equivariant Floer Theory for binary polyhedral spaces \yr\vol\jour Preprint \key AB \by D. Austin and P. Braam \pages\paper Equivariant Floer cohomology \yr\vol\jour Topology (To appear) \key BDGW \by S. Bradlow, G. Daskalopoulos, O. Garcia-Prada, R. Wentworth \paper Stable augmented bundles over Riemann surfaces \inbook Vector bundles in algebraic geometry (Ed. Hitchin, Newstead, Oxbury)\yr1995 \publ Cambridge UP
  • S. K. Donaldson, Connections, cohomology and the intersection forms of $4$-manifolds, J. Differential Geom. 24 (1986), no. 3, 275–341. MR 868974
  • S. K. Donaldson, Irrationality and the $h$-cobordism conjecture, J. Differential Geom. 26 (1987), no. 1, 141–168. MR 892034
  • S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), no. 3, 257–315. MR 1066174, DOI
  • \key D4 \by S. Donaldson \paper Yang-Mills invariants of four-manifolds \inbook Geometry of low-dimensional manifolds, Vol I (Ed. Donaldson and Thomas) \publ Cambridge UP \yr1990
  • S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1990. Oxford Science Publications. MR 1079726
  • S. K. Donaldson and D. P. Sullivan, Quasiconformal $4$-manifolds, Acta Math. 163 (1989), no. 3-4, 181–252. MR 1032074, DOI
  • \ref\key E \by N. Elkies \paper A characterisation of the $\mathbf {Z}^{n}$-lattice \jour Math. Res. Letters \yr To appear \key FS \by R. Fintushel and R. Stern \paper The blowup formula for Donaldson invariants \yr1994 \vol\jour Preprint
  • Robert Friedman and John W. Morgan, Algebraic surfaces and $4$-manifolds: some conjectures and speculations, Bull. Amer. Math. Soc. (N.S.) 18 (1988), no. 1, 1–19. MR 919651, DOI
  • \key FQ \by R. Friedman and Z. Qin \pages369-376 \paper The smooth invariance of the Kodaira dimension of a complex surface \yr1994 \vol1 \jour Math. Res. Letters \key Go \by R. Gompf \pages\paper A new construction of symplectic manifolds \yr1994 \vol\jour Preprint \ref\key Got \by L. Gottsche\pages\paper Modular forms and Donaldson invariants for $4$-manifolds with $b_{+}=1$ \yr1995 \jour Preprint
  • M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718, DOI
  • Mikhael Gromov and H. Blaine Lawson Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 111 (1980), no. 3, 423–434. MR 577131, DOI
  • N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), no. 1, 59–126. MR 887284, DOI
  • Arthur Jaffe and Clifford Taubes, Vortices and monopoles, Progress in Physics, vol. 2, Birkhäuser, Boston, Mass., 1980. Structure of static gauge theories. MR 614447
  • Peter B. Kronheimer, Embedded surfaces in $4$-manifolds, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 529–539. MR 1159240
  • \ref\key KL \by D. Kotschick and P.Lisca \paper Instanton invariants of $\mathbf {C}\mathbf {P}^{2}$ via topology \jour preprint
  • P. B. Kronheimer and T. S. Mrowka, Gauge theory for embedded surfaces. I, Topology 32 (1993), no. 4, 773–826. MR 1241873, DOI
  • 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
  • \ref\key KM3 \by P. Kronheimer and T. Mrowka\pages797-808 \paper The genus of embedded surfaces in the projective plane \yr1994 \vol1 \jour Math. Res. Letters \key L \by C. LeBrun \pages1-8 \paper Einstein metrics and Mostow rigidity \yr1995 \vol2 \jour Math. Res. Letters \ref\key M \by M. Manetti \pages285-297 \paper On some components of moduli spaces of surfaces of general type \yr1994 \vol92 \jour Compositio Math. \ref\key MST \by J. Morgan, Z. Szabo and C. Taubes \paper The generalised Thom conjecture \jour In preparation \ref\key PT \by V. Pidstragach and A. Tyurin \paper Invariants of the smooth structure of an algebraic surface arising from the Dirac operator (English translation) \yr1994 \vol\jour Russian Math. Surveys
  • V. Ya. Pidstrigach and A. N. Tyurin, The smooth structure invariants of an algebraic surface defined by the Dirac operator, Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), no. 2, 279–371 (Russian, with Russian summary); English transl., Russian Acad. Sci. Izv. Math. 40 (1993), no. 2, 267–351. MR 1180377, DOI
  • \key SW \by N. Seiberg and E. Witten \pages581-640 \paper Monopoles, duality and chiral symmetry breaking in $N=2$ supersymmetric QCD \yr1994 \vol431 \jour Nucl. Phys. B \ref\key St \by A. Stipsicz \paper Donaldson invariants of certain symplectic $4$-manifolds \yr\vol\jour Crelles Journal (To appear) \ref\key Su \by D. Sullivan \paper Exterior $d$, the local index and smoothability \yr1995 \vol\jour IHES preprint \key T1 \by C. Taubes \pages809-822 \paper The Seiberg-Witten invariants and symplectic forms \yr1994 \vol1 \jour Math. Res. Letters \ref\key T2 \by C. Taubes \pages9-14 \paper More constraints on symplectic forms from Seiberg-Witten equations \yr1995 \vol2 \jour Math. Res. Letters \ref\key T3 \by C. Taubes \paper The Seiberg-Witten and the Gromov invariants \yr1995 \vol\jour Harvard Preprint
  • Michael Thaddeus, Stable pairs, linear systems and the Verlinde formula, Invent. Math. 117 (1994), no. 2, 317–353. MR 1273268, DOI
  • \key VW \by C. Vafa and E. Witten \paper A strong coupling test of S-duality\jour Nucl. Phys. B (To appear)
  • Edward Witten, Topological quantum field theory, Comm. Math. Phys. 117 (1988), no. 3, 353–386. MR 953828
  • \key W2 \by E. Witten \paper Supersymmetric Yang-Mills theory on a four-manifold \yr1994 \vol35 \jour J. Math. Phys. \ref\key W3 \by E. Witten \pages769-796 \paper Monopoles and 4-manifolds \yr1994 \vol1 \jour Math. Res. Letters

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Additional Information

S. K. Donaldson
Affiliation: The Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford OX1 3LB, England

Received by editor(s): May 15, 1995
Article copyright: © Copyright 1996 American Mathematical Society