The Seiberg-Witten equations and 4-manifold topology
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References
- M. F. Atiyah and L. Jeffrey, Topological Lagrangians and cohomology, J. Geom. Phys. 7 (1990), no. 1, 119–136. MR 1094734, DOI 10.1016/0393-0440(90)90023-V \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, DOI 10.4310/jdg/1214440551
- S. K. Donaldson, Irrationality and the $h$-cobordism conjecture, J. Differential Geom. 26 (1987), no. 1, 141–168. MR 892034, DOI 10.4310/jdg/1214441179
- S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), no. 3, 257–315. MR 1066174, DOI 10.1016/0040-9383(90)90001-Z \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 10.1007/BF02392736 \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 10.1090/S0273-0979-1988-15576-0 \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 10.1007/BF01388806
- 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 10.2307/1971103
- 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 10.1112/plms/s3-55.1.59
- 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 10.1016/0040-9383(93)90051-V
- 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 \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 10.1070/IM1993v040n02ABEH002167 \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 10.1007/BF01232244 \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, DOI 10.1007/BF01223371 \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
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
- Received by editor(s): May 15, 1995
- © Copyright 1996 American Mathematical Society
- 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