Monopôles de Seiberg-Witten et conjecture de Thom

Bennequin, Daniel

Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 807, 38 p.

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     author = {Bennequin, Daniel},
     title = {Monop\^oles de {Seiberg-Witten} et conjecture de {Thom}},
     booktitle = {S\'eminaire Bourbaki : volume 1995/96, expos\'es 805-819},
     series = {Ast\'erisque},
     note = {talk:807},
     pages = {59--96},
     year = {1997},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {241},
     mrnumber = {1472535},
     zbl = {0881.57035},
     language = {fr},
     url = {https://www.numdam.org/item/SB_1995-1996__38__59_0/}
}

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Bennequin, Daniel. Monopôles de Seiberg-Witten et conjecture de Thom, dans Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 807, 38 p.. https://www.numdam.org/item/SB_1995-1996__38__59_0/

Bibliographie
Cité par

[A] M. F. Atiyah - Classical groups and classical differential operators on manifolds, CIME, Varenna (1975), 6-48. | MR

[ABP] M. F. Atiyah, R. Bott, V. K. Patodi - On the heat equation and the index theorem, Invent. Math. 19 (1973), 279-330 et 28 (1975), 277-280. | Zbl | MR | EuDML | DOI

[ABS] M. F. Atiyah, R. Bott, A. Shapiro - Clifford modules, Topology 3, suppl. 1 (1964), 3-38. | Zbl | MR | DOI

[AHS] M. F. Atiyah, N. J. Hitchin, I. M. Singer - Self-duality in four dimensional Riemannian Geometry, Proc. Royal Soc. London 362 (1978), 425-461. | Zbl | MR | DOI

[APS] M. F. Atiyah, V. K. Patodi, I. M. Singer - Spectral asymmetry and Riemannian Geometry, I, Math. Proc. Camb. Phil. Soc. 77 (1975), 43-69. | Zbl | MR | DOI

[AS] M. F. Atiyah, I. M. Singer - The index of elliptic operators, III, Ann. of Math. 87 (1968), 546-604. | Zbl | MR | DOI

[Au] D. Auckley - Surgery, knots and the Seiberg-Witten equations, preprint, Berkeley, 1995.

[B1] D. Bennequin - Problèmes elliptiques, surfaces de Riemann et structures symplectiques [d'après M. Gromov], Sém. Bourbaki, exp. n° 657, février 1986, Astérisque 145-146 (1987), 111-136. | Numdam | Zbl | MR | EuDML

[B2] D. Bennequin - Topologie symplectique, convexité holomorphe et structures de contact [d'après Y. Eliashberg, D. Mc Duff et al.], Sém. Bourbaki, exp. n° 725, juin 1990, Astérisque 189-190 (1990), 285-323. | Numdam | Zbl | MR | EuDML

[B3] D. Bennequin - L'instanton gordien, Sém. Bourbaki, exp. n° 770, juin 1993, Astérisque 216 (1993), 233-277. | Numdam | Zbl | MR | EuDML

[BWe] M. Boileau, C. Weber - Le problème de J. Milnor sur le nombre gordien des nœuds algébriques, Ens. Math. 30 (1984), 173-222. | Zbl

[Bbk] N. Bourbaki - Algèbre, ch. IX, Hermann, Paris, 1959. | Zbl

[Be] A. Besse - Géométrie riemannienne en dimension 4 (exposés de J.-P. Bourguignon, J. Lafontaine, P. Marry), CEDIC, Nathan, Paris, 1981. | MR

[Bo] A. Borel - Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Thèse, Paris, 1952, Ann. of Math. (2) 57 (1953), 115-207. | Zbl | MR

[Bou] J.-P. Bourguignon - The magic of Weitzenböck formulas, in : Variational methods, progress in nonlinear differential equations and their applications, Boston (1990), 251-273. | Zbl | MR

[CaGo] R. N. Cahn et G. Goldhaber - The experimental foundations of particle physics, Cambridge U.P., 1989.

[C] É. Cartan - The theory of spinors, Hermann, Paris, 2ème éd., 1966. | Zbl

[Ch] S. S. Chern - Complex manifolds without potential theory, Springer, 2ème éd., 1979. | Zbl | MR

[dR] C. De Rham - Variétés différentiables, Herman, Paris, 3ème éd., 1973. | Zbl | MR

[Di] P. A. M. Dirac - The principles of quantum mechanics, 4ème édition, Oxford, 1967. | Zbl | MR

[D1] S. K. Donaldson - Connexions, cohomology and the intersection forms of four-manifolds, J. of Diff. Geom. 24 (1986), 275-341. | Zbl | MR | DOI

[D2] S. K. Donaldson - Irrationality and the $h$ -cobordism conjecture, J. of Diff. Geom. 26 (1987), 141-168. | Zbl | MR | DOI

[D3] S. K. Donaldson - The orientation of Yang-Mills moduli spaces and 4-manifold topology, J. of Diff. Geom. 26 (1987), 397-428. | Zbl | MR | DOI

[D4] S. K. Donaldson - Polynomial invariants for smooth four-manifolds, Topology 29 (1990), 257-315. | Zbl | MR | DOI

[DK] S. K. Donaldson and P. B. Kronheimer - The geometry of four-manifolds, Oxford University Press (1990). | Zbl | MR

[DuSp] C. D. Duff, D. C. Spencer - Harmonic tensors on riemannian manifolds with boundary, Ann. of Math. 56 (1952), 128-196. | Zbl | MR | DOI

[EF] J. Eichhorn, T. Friedrich - Seiberg-Witten theory, 1995, Preprint, Berlin. | MR | Zbl

[F] R. P. Feynman - Lectures on Physics, Caltec, 1965. | Zbl

[Gau] P. Gauduchon - Variétés riemanniennes autoduales (d'après C.H. Taubes et al.), Sém. Bourbaki, exp. n° 767, mars 1993, Astérisque 216 (1993), 151-186. | Numdam | Zbl | MR | EuDML

[G] M. Gromov - Pseudo-holomorphic curves on almost complex manifolds, Invent. Math. 82 (1985), 307-347. | Zbl | EuDML | MR | DOI

[GL1] M. Gromov, H. B. Lawson - The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980), 423-434. | Zbl | MR | DOI

[GL2] M. Gromov, H. B. Lawson - Spin and scalar curvature in the presence of a fundamental group, I, Ann. of Math. 111 (1980), 209-230. | Zbl | MR | DOI

[H] N. Hitchin - Harmonic spinors, Adv. in Math. 14 (1974), 1-55. | Zbl | MR | DOI

[HiHo] F. Hirzebruch, H. Hopf - Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten, Math. Annalen 136 (1958), 156-172. | Zbl | MR | EuDML | DOI

[HsSz] W. C. Hsiang, R. H. Szczarba - On embedding surfaces in four-manifolds, In : Algebraic Topology, Proc. Sympos. Pure Math., vol. 22, Americ. Math. Soc., Providence, R.I., 1971, 97-103. | Zbl | MR | DOI

[IZ] C. Itzykson et J.-B. Zuber - Quantum field theory, Mc Graw Hill, 1980. | MR | Zbl

[KeMi] M. Kervaire, J. Milnor - On 2-spheres in 4-manifolds, Proc. Nat. Acad. Science USA 47 (1961), 1651-1657. | Zbl | MR | DOI

[KM1] P. B. Kronheimer, T. S. Mrowka - Gauge theory for embedded surfaces, I, Topology, 1994, II, Topology, 1995. | Zbl | MR

[KM2] P. B. Kronheimer, T. S. Mrowka - Embedded surfaces and the structure of Donaldson's polynomial invariants, J. of Diff. Geom., 1995. | Zbl

[KM3] P. B. Kronheimer, T. S. Mrowka - The genus of embedded surfaces in the projective plane, Math. Res. Letters 1 (1994), 798-808. | Zbl | MR | DOI

[KoMa] D. Kotschick, G. Matic - Embedded surfaces in four-manifolds, branched covers and SO(3)-invariants, Preprint Bâle (1993). | MR | Zbl

[LM] B. Lawson, M. Michelson - Spin geometry, Princeton Univ. Press, 1989. | Zbl | MR

[Li] A. Lichnerowicz - Spineurs harmoniques, CRAS 257 (1963). | Zbl | MR

[Mi1] J. W. Milnor - Spin structures on manifolds, L'Ens. Math. 9 (1963), 198-203. | Zbl | MR

[Mi2] J. W. Milnor - Remarks concerning Spin manifolds, In : Differential and combinatorial topology : A symposium in honor of Marston Morse, Princeton Univ. Press (1965), 55-62. | Zbl | MR

[MiSt] J. W. Milnor, J. D. Stasheff - Characteristic classes, Princeton Univ. Press, New Jersey, 1974. | Zbl | MR

[PR] R. Penrose, W. Rindler - Spinors and space-time, vol. 1, Cambridge, 86 (1984). | Zbl | MR

[Ro] V. A. Rohlin - Two-dimensional submanifolds of four-dimensional manifolds, Funct. Anal. Appl. 5 (1971), 39-48. | Zbl | MR | DOI

[SWi1] N. Seiberg, E. Witten - Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nuclear Physics B 426 (1994), 19-52. | Zbl | MR | DOI

[SWi2] N. Seiberg, E. Witten - Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nuclear Physics B 431 (1994), 484-550. | Zbl | MR | DOI

[Tl] C. Taubes - The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1 (1994), 809-822. | Zbl | MR | DOI

[T2] C. Taubes - More constraints on symplectic manifolds from the Seiberg-Witten invariants, Math. Res. Letters 2 (1995), 9-14. | Zbl | MR | DOI

[T3] C. Taubes - The Seiberg-Witten and the Gromov invariants, Math. Res. Letters 2 (1995), 221-238. | Zbl | MR | DOI

[Th1] R. Thom - Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86. | Zbl | MR | EuDML | DOI

[Th2] R. Thom - Stabilité structurelle et morphogénèse, Interéditions, 2ème édition, Paris, 1977. | Zbl

[Th3] R. Thom - Spectre bord d'un centre obscur, dans : "Passion des formes" (M. Porte, coordonnateur), Fontenay-Saint Cloud (1994), 13-23.

[Wa] Wang Shuguang - A vanishing theorem for Seiberg-Witten invariants, Math. Res. Letters 2 (1995), 305-310. | Zbl | MR | DOI

[WB] J. Wess et J. Bagger - Supersymmetry and supergravity, 2nd edition, Princeton, 1992. | Zbl | MR

[Wh] H. Whitney - On the topology of differentiable manifolds, Lectures in Topology, Univ. of Michigan Press, 1941, 101-141, In : Collected papers, Vol. II, 175-215. | Zbl | MR

[Wil] E. Witten - Topological Quantum Field Theory, Comm. Math. Phys. (1988), 353-386. | Zbl | MR | DOI

[Wi2] E. Witten - Quantum field theory and the Jones polynomials , Comm. Math. Phys. 121 (1989), 351-399. | Zbl | MR | DOI

[Wi3] E. Witten - Supersymmetric Yang-Mills theory on a four-manifold, Preprint IAS, 1994. | MR | Zbl

[Wi4] E. Witten - Monopoles and 4-manifolds, Math. Res. Letters 1 (1994), 769-796. | Zbl | MR | DOI

[Wu] Wu Wen Tsun - Sur la structure presque complexe d'une variété différentiable réelle de dimension 4, Note CRAS, 15 nov. 1948, 1076-1078. | Zbl | MR