Monopôles de Seiberg-Witten et conjecture de Thom

Daniel Bennequin

Séminaire Bourbaki (1995-1996)

  • Volume: 38, page 59-96
  • ISSN: 0303-1179

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Bennequin, Daniel. "Monopôles de Seiberg-Witten et conjecture de Thom." Séminaire Bourbaki 38 (1995-1996): 59-96. <http://eudml.org/doc/110223>.

@article{Bennequin1995-1996,
author = {Bennequin, Daniel},
journal = {Séminaire Bourbaki},
keywords = {spin structures; Clifford algebra; Seiberg-Witten equations},
language = {fre},
pages = {59-96},
publisher = {Société Mathématique de France},
title = {Monopôles de Seiberg-Witten et conjecture de Thom},
url = {http://eudml.org/doc/110223},
volume = {38},
year = {1995-1996},
}

TY - JOUR
AU - Bennequin, Daniel
TI - Monopôles de Seiberg-Witten et conjecture de Thom
JO - Séminaire Bourbaki
PY - 1995-1996
PB - Société Mathématique de France
VL - 38
SP - 59
EP - 96
LA - fre
KW - spin structures; Clifford algebra; Seiberg-Witten equations
UR - http://eudml.org/doc/110223
ER -

References

top
  1. [A] M.F. Atiyah - Classical groups and classical differential operators on manifolds, CIME, Varenna (1975), 6-48. MR650830
  2. [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. Zbl0257.58008MR650828
  3. [ABS] M.F. Atiyah, R. Bott, A. Shapiro - Clifford modules, Topology3, suppl. 1 (1964), 3-38. Zbl0146.19001MR167985
  4. [AHS] M.F. Atiyah, N.J. Hitchin, I.M. Singer - Self-duality in four dimensional Riemannian Geometry, Proc. Royal Soc. London362 (1978), 425-461. Zbl0389.53011MR506229
  5. [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. Zbl0297.58008MR397797
  6. [AS] M.F. Atiyah, I.M. Singer - The index of elliptic operators, III, Ann. of Math.87 (1968), 546-604. Zbl0164.24301MR236952
  7. [Au] D. Auckley - Surgery, knots and the Seiberg-Witten equations, preprint, Berkeley, 1995. 
  8. [B1] D. Bennequin - Problèmes elliptiques, surfaces de Riemann et structures symplectiques [d'après M. Gromov], Sém. Bourbaki, exp. n° 657, février 1986, Astérisque145-146 (1987), 111-136. Zbl0644.53031MR880029
  9. [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, Astérisque189-190 (1990), 285-323. Zbl0755.32009MR1099880
  10. [B3] D. Bennequin - L'instanton gordien, Sém. Bourbaki, exp. n° 770, juin 1993, Astérisque216 (1993), 233-277. Zbl0799.57008MR1246400
  11. [BWe] M. Boileau, C. Weber - Le problème de J. Milnor sur le nombre gordien des nœuds algébriques, Ens. Math.30 (1984), 173-222. Zbl0556.57002
  12. [Bbk] N. Bourbaki - Algèbre, ch. IX, Hermann, Paris, 1959. 
  13. [Be] A. Besse - Géométrie riemannienne en dimension 4 (exposés de J.-P. Bourguignon, J. Lafontaine, P. Marry), CEDIC, Nathan, Paris, 1981. MR769127
  14. [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. Zbl0052.40001MR51508
  15. [Bou] J.-P. Bourguignon - The magic of Weitzenböck formulas, in : Variational methods, progress in nonlinear differential equations and their applications, Boston (1990), 251-273. Zbl0774.35003MR1205158
  16. [CaGo] R.N. Cahn et G. Goldhaber - The experimental foundations of particle physics, Cambridge U.P., 1989. 
  17. [C] É. Cartan - The theory of spinors, Hermann, Paris, 2ème éd., 1966. Zbl0147.40101
  18. [Ch] S.S. Chern - Complex manifolds without potential theory, Springer, 2ème éd., 1979. Zbl1101.32301MR533884
  19. [dR] C. De Rham - Variétés différentiables, Herman, Paris, 3ème éd., 1973. Zbl0284.58001
  20. [Di] P.A.M. Dirac - The principles of quantum mechanics, 4ème édition, Oxford, 1967. Zbl0012.18104MR23198
  21. [D1] S.K. Donaldson - Connexions, cohomology and the intersection forms of four-manifolds, J. of Diff. Geom.24 (1986), 275-341. Zbl0635.57007MR868974
  22. [D2] S.K. Donaldson - Irrationality and the h-cobordism conjecture, J. of Diff. Geom.26 (1987), 141-168. Zbl0631.57010MR892034
  23. [D3] S.K. Donaldson - The orientation of Yang-Mills moduli spaces and 4-manifold topology, J. of Diff. Geom.26 (1987), 397-428. Zbl0683.57005MR910015
  24. [D4] S.K. Donaldson - Polynomial invariants for smooth four-manifolds, Topology29 (1990), 257-315. Zbl0715.57007MR1066174
  25. [DK] S.K. Donaldson and P.B. Kronheimer - The geometry of four-manifolds, Oxford University Press (1990). Zbl0820.57002MR1079726
  26. [DuSp] C.D. Duff, D.C. Spencer - Harmonic tensors on riemannian manifolds with boundary, Ann. of Math.56 (1952), 128-196. Zbl0049.18901MR48137
  27. [EF] J. Eichhorn, T. Friedrich - Seiberg-Witten theory, 1995, Preprint, Berlin. MR1458664
  28. [F] R.P. Feynman - Lectures on Physics, Caltec, 1965. 
  29. [Gau] P. Gauduchon - Variétés riemanniennes autoduales (d'après C.H. Taubes et al.), Sém. Bourbaki, exp. n° 767, mars 1993, Astérisque216 (1993), 151-186. Zbl0789.53026MR1246397
  30. [G] M. Gromov - Pseudo-holomorphic curves on almost complex manifolds, Invent. Math.82 (1985), 307-347. Zbl0592.53025MR1554036
  31. [GL1] M. Gromov, H.B. Lawson - The classification of simply connected manifolds of positive scalar curvature, Ann. of Math.111 (1980), 423-434. Zbl0463.53025MR577131
  32. [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. Zbl0445.53025MR569070
  33. [H] N. Hitchin - Harmonic spinors, Adv. in Math.14 (1974), 1-55. Zbl0284.58016MR358873
  34. [HiHo] F. Hirzebruch, H. Hopf - Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten, Math. Annalen136 (1958), 156-172. Zbl0088.39403MR100844
  35. [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. Zbl0234.57009MR339239
  36. [IZ] C. Itzykson et J.-B. Zuber - Quantum field theory, Mc Graw Hill, 1980. MR585517
  37. [KeMi] M. Kervaire, J. Milnor - On 2-spheres in 4-manifolds, Proc. Nat. Acad. Science USA47 (1961), 1651-1657. Zbl0107.40303MR133134
  38. [KM1] P.B. Kronheimer, T.S. Owka - Gauge theory for embedded surfaces, I, Topology, 1994, II, Topology, 1995. 
  39. [KM2] P.B. Kronheimer, T.S. Owka - Embedded surfaces and the structure of Donaldson's polynomial invariants, J. of Diff. Geom., 1995. Zbl0842.57022
  40. [KM3] P.B. Kronheimer, T.S. Owka - The genus of embedded surfaces in the projective plane, Math. Res. Letters1 (1994), 798-808. Zbl0851.57023MR1306022
  41. [KoMa] D. Kotschick, G. Matic - Embedded surfaces in four-manifolds, branched covers and SO(3)-invariants, Preprint Bâle (1993). MR1307081
  42. [LM] B. Lawson, M. Michelson - Spin geometry, Princeton Univ. Press, 1989. Zbl0688.57001MR1031992
  43. [Li] A. Lichnerowicz - Spineurs harmoniques, CRAS257 (1963). Zbl0136.18401MR156292
  44. [Mi1] J.W. Milnor - Spin structures on manifolds, L'Ens. Math.9 (1963), 198-203. Zbl0116.40403MR157388
  45. [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. Zbl0132.19602MR180978
  46. [MiSt] J.W. Milnor, J.D. Stasheff - Characteristic classes, Princeton Univ. Press, New Jersey, 1974. Zbl0298.57008MR440554
  47. [PR] R. Penrose, W. Rindler - Spinors and space-time, vol. 1, Cambridge, 86 (1984). Zbl0538.53024MR776784
  48. [Ro] V.A. Rohlin - Two-dimensional submanifolds of four-dimensional manifolds, Funct. Anal. Appl.5 (1971), 39-48. Zbl0268.57019MR298684
  49. [SWi1] N. Seiberg, E. Witten - Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nuclear Physics B426 (1994), 19-52. Zbl0996.81510MR1293681
  50. [SWi2] N. Seiberg, E. Witten - Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nuclear Physics B431 (1994), 484-550. Zbl1020.81911MR1306869
  51. [Tl] C. Taubes - The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters1 (1994), 809-822. Zbl0853.57019MR1306023
  52. [T2] C. Taubes - More constraints on symplectic manifolds from the Seiberg-Witten invariants, Math. Res. Letters2 (1995), 9-14. Zbl0854.57019MR1312973
  53. [T3] C. Taubes - The Seiberg-Witten and the Gromov invariants, Math. Res. Letters2 (1995), 221-238. Zbl0854.57020MR1324704
  54. [Th1] R. Thom - Quelques propriétés globales des variétés différentiables, Comment. Math. Helv.28 (1954), 17-86. Zbl0057.15502MR61823
  55. [Th2] R. Thom - Stabilité structurelle et morphogénèse, Interéditions, 2ème édition, Paris, 1977. Zbl0365.92001
  56. [Th3] R. Thom - Spectre bord d'un centre obscur, dans : "Passion des formes" (M. Porte, coordonnateur), Fontenay-Saint Cloud (1994), 13-23. 
  57. [Wa] Wang Shuguang - A vanishing theorem for Seiberg-Witten invariants, Math. Res. Letters2 (1995), 305-310. Zbl0841.57042MR1338789
  58. [WB] J. Wess et J. Bagger - Supersymmetry and supergravity, 2nd edition, Princeton, 1992. Zbl0516.53060MR1152804
  59. [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. Zbl0063.08233MR5300
  60. [Wil] E. Witten - Topological Quantum Field Theory, Comm. Math. Phys. (1988), 353-386. Zbl0656.53078MR953828
  61. [Wi2] E. Witten - Quantum field theory and the Jones polynomials , Comm. Math. Phys.121 (1989), 351-399. Zbl0667.57005MR990772
  62. [Wi3] E. Witten - Supersymmetric Yang-Mills theory on a four-manifold, Preprint IAS, 1994. MR1295460
  63. [Wi4] E. Witten - Monopoles and 4-manifolds, Math. Res. Letters1 (1994), 769-796. Zbl0867.57029MR1306021
  64. [Wu] Wu Wen Tsun - Sur la structure presque complexe d'une variété différentiable réelle de dimension 4, Note CRAS, 15 nov. 1948, 1076-1078. Zbl0037.10304MR27515

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