An application of gauge theory to four-dimensional topology
S. K. Donaldson
Source: J. Differential Geom. Volume 18, Number 2
(1983), 279-315.
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Mathematical Reviews number (MathSciNet): MR710056
Zentralblatt MATH identifier: 0507.57010
References
[1] M. F. Atiyah, K-Theory, Benjamin, New York, 1967.
Mathematical Reviews (MathSciNet): MR224083
[2] M. F. Atiyah, N. J. Hitchin and I. M. Singer, Self-duality in four dimensional Riemannian geometry, Proc. Roy. Soc. London A 362 (1978) 425-461.
Zentralblatt MATH: 0389.53011
Mathematical Reviews (MathSciNet): MR506229
Digital Object Identifier: doi:10.1098/rspa.1978.0143
[3] M. F. Atiyah and J. D. S. Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978) 97-118.
Zentralblatt MATH: 0387.55009
Mathematical Reviews (MathSciNet): MR503187
Digital Object Identifier: doi:10.1007/BF01609489
Project Euclid: euclid.cmp/1103904210
[4] M. F. Atiyah and I. M. Singer, The index of elliptic operators. IV, Ann. of Math. 93 (1971) 119-138.
Zentralblatt MATH: 0212.28603
Mathematical Reviews (MathSciNet): MR279833
Digital Object Identifier: doi:10.2307/1970756
JSTOR: links.jstor.org
[5] J. P. Bourguignon and H. B. Lawson, Jr., Yang-Mills theory: physical origins and differential geometric aspects, Annals of Math. Studies, No. 102, Princeton University Press, Princeton, 1982, 395-421.
Zentralblatt MATH: 0482.58007
[6] S. S. Chern, Complex manifolds without potential theory, Math. Studies No. 15, Van Nostrand, Princeton, 1967.
Zentralblatt MATH: 0158.33002
Mathematical Reviews (MathSciNet): MR225346
[7] S. K. Donaldson, Self-dual connections and the topology of smooth -manifolds, Bull. Amer. Math. Soc. 8 (1983), 81-83.
Zentralblatt MATH: 0519.57012
Mathematical Reviews (MathSciNet): MR682827
Digital Object Identifier: doi:10.1090/S0273-0979-1983-15090-5
Project Euclid: euclid.bams/1183550021
[8] M. H. Freedman, The topology of four-dimensional manifold J. Differential Geometry 17 (1982) 357-453.
Zentralblatt MATH: 0528.57011
Mathematical Reviews (MathSciNet): MR679066
Project Euclid: euclid.jdg/1214437136
[9] W. V. D. Hodge, The theory and applications of harmonic integrals, Cambridge University Press, Cambridge, 1952.
Zentralblatt MATH: 0048.15702
Mathematical Reviews (MathSciNet): MR51571
[10] M. Kuranishi, A new proof for the existence of locally complete families of complex structures, Proc. Complex Analysis (Minneapolis), Springer, Berlin, 1964, 142-156.
Zentralblatt MATH: 0144.21102
Mathematical Reviews (MathSciNet): MR176496
[11] R. Mandelbaum, Four dimensional topology: an introduction, Bull. Amer. Math. Soc. 2 (1980) 1-159.
Zentralblatt MATH: 0476.57005
Mathematical Reviews (MathSciNet): MR551752
Digital Object Identifier: doi:10.1090/S0273-0979-1980-14687-X
Project Euclid: euclid.bams/1183545202
[12] J. W. Milnor, On simply connected 4-manifolds, Proc. Internat. Sympos. on Algebraic Topology, University of Mexico, 1958, 122-128.
Zentralblatt MATH: 0105.17204
Mathematical Reviews (MathSciNet): MR103472
[13] T. Parker, Gauge theories on A-dimensional Riemannian manifolds, Comm. Math. Phys. 85 (1982) 563-602.
Zentralblatt MATH: 0502.53022
Mathematical Reviews (MathSciNet): MR677998
Digital Object Identifier: doi:10.1007/BF01403505
Project Euclid: euclid.cmp/1103921548
[14] J. Saks and K. K. Uhlenbeck, On the existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1982) 1-24.
Zentralblatt MATH: 0462.58014
Mathematical Reviews (MathSciNet): MR604040
Digital Object Identifier: doi:10.2307/1971131
[15] S. Sedlacek, A direct method for minimising the Yang-Mills functional, Comm. Math. Phys. 86 (1982) 515-528.
Zentralblatt MATH: 0506.53016
Mathematical Reviews (MathSciNet): MR679200
Digital Object Identifier: doi:10.1007/BF01214887
Project Euclid: euclid.cmp/1103921842
[16] J. P. Serre, A course in arithmetic, Springer, Berlin, 1973.
Zentralblatt MATH: 0256.12001
Mathematical Reviews (MathSciNet): MR344216
[17] S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965) 861-866.
Zentralblatt MATH: 0143.35301
Mathematical Reviews (MathSciNet): MR185604
Digital Object Identifier: doi:10.2307/2373250
JSTOR: links.jstor.org
[18] C. H. Taubes, Self-dual connections on non-self-dual 4-manifolds, J. Differential Geometry 17 (1982) 139-170.
Zentralblatt MATH: 0484.53026
Mathematical Reviews (MathSciNet): MR658473
Project Euclid: euclid.jdg/1214436701
[19] C. H. Taubes, Private letter.
[20] K. K. Uhlenbeck, Removeable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982) 11-30.
Zentralblatt MATH: 0491.58032
Mathematical Reviews (MathSciNet): MR648355
Digital Object Identifier: doi:10.1007/BF01947068
Project Euclid: euclid.cmp/1103920742
[21] K. K. Uhlenbeck, Connections with Lp bounds on curvature, Comm. Math. Phys. 83 (1982) 31-42.
Zentralblatt MATH: 0499.58019
Mathematical Reviews (MathSciNet): MR648356
Digital Object Identifier: doi:10.1007/BF01947069
Project Euclid: euclid.cmp/1103920743
[22] J. H. C. Whitehead, Onsimply connected 4-dimensional polyhedra, Comment. Math. Helv. 22 (1949) 48-92.
Zentralblatt MATH: 0036.12704
Mathematical Reviews (MathSciNet): MR29171
Digital Object Identifier: doi:10.1007/BF02568048
Journal of Differential Geometry