L'instanton gordien

Daniel Bennequin

Séminaire Bourbaki (1992-1993)

  • Volume: 35, page 233-277
  • ISSN: 0303-1179

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Bennequin, Daniel. "L'instanton gordien." Séminaire Bourbaki 35 (1992-1993): 233-277. <http://eudml.org/doc/110171>.

@article{Bennequin1992-1993,
author = {Bennequin, Daniel},
journal = {Séminaire Bourbaki},
keywords = {gauge theory; algebraic knots; local Thom conjecture; genus of a surface representing a given 2-dimensional homology class; smooth simply- connected 4-manifold; polynomial invariants; slice genus; unknotting number; genus of the Milnor fibre},
language = {fre},
pages = {233-277},
publisher = {Société Mathématique de France},
title = {L'instanton gordien},
url = {http://eudml.org/doc/110171},
volume = {35},
year = {1992-1993},
}

TY - JOUR
AU - Bennequin, Daniel
TI - L'instanton gordien
JO - Séminaire Bourbaki
PY - 1992-1993
PB - Société Mathématique de France
VL - 35
SP - 233
EP - 277
LA - fre
KW - gauge theory; algebraic knots; local Thom conjecture; genus of a surface representing a given 2-dimensional homology class; smooth simply- connected 4-manifold; polynomial invariants; slice genus; unknotting number; genus of the Milnor fibre
UR - http://eudml.org/doc/110171
ER -

References

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  1. [A1] M.F. Atiyah - Magnetic monopoles in hyperbolic spaces, Vector bundles on algebraic varieties, Tata Institute of Fundamental Research, Bombay (1984), 1-33. Zbl0722.53063MR893593
  2. [A2] M.F. Atiyah - New invariants of 3 and 4-dimensional manifolds, in "Symposium on the mathematical heritage of Hermann-Weyl", University of North Carolina, Ed. R. Wells & al. (1987). 
  3. [A3] M.F. Atiyah - The Jones-Witten invariant of knots, Sém. Bourbaki, exp. n° 715, novembre 1989, Astérisque189-190 (1990), 7-16. Zbl0739.57001MR1099870
  4. [A4] M.F. Atiyah - K-theory, Benjamin, New York (1967). MR224083
  5. [AHS] M.F. Atiyah, N.J. Hitchin and I.M. Singer - Self-duality in four dimensional Riemannian Geometry, Proc. Royal Soc. London362 (1978), 425-461. Zbl0389.53011MR506229
  6. [APS] M.F. Atiyah, V.K. Patodi and I.M. Singer - Spectral asymmetry and Riemannian Geometry, I, Math. Proc. Camb. Phil. Soc.77 (1975), 43-69. II, Math. Proc. Camb. Phil. Soc.78 (1975), 405-432. III, Math. Proc. Camb. Phil. Soc.79 (1976), 71-99. Zbl0314.58016MR397797
  7. [B1] O. Biquard - Fibrés holomorphes et connexions singulières sur une courbe ouverte, Thèse, École Polytechnique (1991). 
  8. [B2] O. Biquard - Sur les fibrés paraboliques sur une surface complexe, preprint (février 1993). MR1373062
  9. [BD] P.J. Braam and S.K. Donaldson - Fukaya-Floer homology and gluing formulae for polynomial invariants, Preprint. Zbl0996.57517MR1362830
  10. [BW] M. Boileau et C. Weber - Le problème de J. Milnor sur le nombre gordien des nœuds algébriques, Ens. Math.30 (1984), 173-222. Zbl0556.57002
  11. [De] P. Dedecker - Sur la cohomologie non-abélienne, I, Canad. J. Math. (1960), 231-251 ; II , Canad. J. Math. (1963), 84-93. Zbl0112.37902MR111021
  12. [D1] S.K. Donaldson - An application of gauge theory to four dimensional topology, J. of Diff. Geometry18 (1983), 279-315. Zbl0507.57010MR710056
  13. [D2] S.K. Donaldson - The orientation of Yang-Mills moduli spaces and 4- manifold topology, J. of Diff. Geometry26 (1987), 397-428. Zbl0683.57005MR910015
  14. [D3] S.K. Donaldson - Connexions, cohomology and the intersection forms of four-manifolds, J. of Diff. Geometry24 (1986), 275-341. Zbl0635.57007MR868974
  15. [D4] S.K. Donaldson - Polynomial invariants for smooth four-manifolds, Topology29 (1990), 257-315. Zbl0715.57007MR1066174
  16. [D5] S.K. Donaldson - Complex curves and surgery, Publ. Math. IHES68 (1989), 91-97. Zbl0696.57007MR1001449
  17. [D6] S.K. Donaldson - Anti-self-dual Yang-Mills connections on complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc.3 (1985), 1-26. Zbl0529.53018MR765366
  18. [DK] S.K. Donaldson and P.B. Kronheimer - The geometry of four-manifolds, Oxford University Press (1990). Zbl0820.57002MR1079726
  19. [DS] S.K. Donaldson and D.P. Sullivan - Quasiconformal four-manifolds, Acta Math.163 (1990), 181-252. Zbl0704.57008MR1032074
  20. [DT] S.K. Donaldson and C.B. Thomas - Geometry of low-dimensional manifolds, I. Gauge theory and algebraic surfaces, London Math. Soc., Lecture Notes series150, Cambridge University Press (1990). Zbl0715.00017MR1171887
  21. [Fl] A. Floer - An instanton-invariant for 3-manifolds, Comm. Math. Phys.118 (1980), 215-240. Zbl0684.53027MR956166
  22. [FM] R. Friedman and J.L. Morgan - Complex versus differentiable classification of algebraic surfaces, Topology Appl.32, North Holland (1989),135-139. Zbl0694.14013MR1007985
  23. [FMM] R. Friedman, J.L. Morgan and B. Moishezon- On the C∞ invariance of the canonical class of certain algebraic surfaces, B.A.M.S.17 (1987), 283- 286. Zbl0627.57014
  24. [FS] R. Fintushel and R. Stern - SO(3)-connections on the topology of four-manifolds, J. Diff. Geom.20, North Holland (1984), 523-539. Zbl0562.53023MR788294
  25. [FU] D.S. Freed and K.K. Uhlenbeck - Instantons and four-manifolds, M.S.R.I. Publications, Vol. 1, Springer (1984). Zbl0559.57001MR757358
  26. [Fr] J. Frenkel - Cohomologie non-abélienne et espaces fibrés, Bull. Soc. Math. France85 (1957), 135-218. Zbl0082.37702MR98200
  27. [Ga] P. Gauduchon - Variétés riemanniennes autoduales [d'après C.H. Taubes et al.], Sém. Bourbaki, exp. n° 767, mars 1993, Astérisque (à paraître). Zbl0789.53026MR1246397
  28. [Gi] J. Giraud - Cohomologie non-abélienne, Springer Verlag, Berlin-Heidelberg- New York (1971). Zbl0226.14011MR344253
  29. [H] N. Hitchin - The Yang-Mills equation and the topology of 4-manifolds [after Simon K. Donaldson], Sém. Bourbaki, exp. n° 606, février 1983, Astérisque105-106 (1983),167-178. Zbl0533.57007MR728987
  30. [I] L. Illusie - Cohomologie de de Rham et cohomologie étale p-adique [d'après G. Faltings, J.-M. Fontaine et al.], Sém. Bourbaki, exp. n° 726, juin 1990, Astérisque189-190 (1990), 325-374. Zbl0736.14005MR1099881
  31. [Ki] R. Kirby - Problems in low-dimensional topology, Proc. Symp. Pure Math.32 (1978), 273-322. MR520548
  32. [Ko] D. Kotschick - SO(3)-invariants for 4-manifolds with b+2 = 1, Proc. London Math. Soc.63 (1991), 426-448. Zbl0699.53036MR1114516
  33. [KoMa] D. Kotschick and G. Matic - Embedded surfaces in four-manifolds, branched covers and SO(3)-invariants, Preprint Bâle (1993). MR1307081
  34. [K1] P.B. Kronheimer - Embedded surfaces in 4-manifolds, Proc. Intern. Congr. Mathematicians, Kyoto1990, Springer, Vol. I (1991), 527-539. Zbl0746.53041MR1159240
  35. [K2] P.B. Kronheimer - An obstruction to removing intersection points in immersed surfaces, preprint Oxford (mars 1993). MR1432428
  36. [K3] P.B. Kronheimer - The genus-minimizing property of algebraic curves, preprint, à paraître au Bull. Amer. Math. Soc. Zbl0810.57014MR1193539
  37. [KM1] P.B. Kronheimer and T.S. Owka - Gauge theory for embedded surfaces, I, preprint (novembre 1991), à paraître dans Topology. MR1241873
  38. [KM2] P.B. Kronheimer and T.S. Owka - Gauge theory for embedded surfaces, II, preprint (août 1992), à paraître dans Topology. MR1308489
  39. [KM3] P.B. Kronheimer and T.S. Owka - Recurrence relations and asymptotics for four-manifold invariants, preprint (mai 1993), à paraître au Bull. Amer. Math. Soc. 
  40. [L] J. Le Potier - Fibrés de Higgs et systèmes locaux, Sém. Bourbaki, exp. n° 737, novembre 1990, Astérisque201- 202-203 (1991), 221-268. Zbl0762.14011MR1157844
  41. [Li] P. Lisca - On Tori embedded in four-manifolds, J. Diff. Geometry38 (1993), 13-37. Zbl0788.53046MR1231701
  42. [Ma] C. Margerin - Fibrés stables et métriques d'Hermite-Einstein [d'après S.K. Donaldson-K.K. Uhlenbeck-S.T. Yau], Sém. Bourbaki, exp. n° 683 (juin 1987), Astérisque152-153 (1987), 263-283. Zbl0637.53080MR936859
  43. [Mi] J. Milnor - Singular points on complex hypersurfaces, Ann. of Math. Studies61, Princeton University Press (1968). Zbl0184.48405MR239612
  44. [MM] J.W. Morgan and T.S. Owka - A note on Donaldson's polynomial invariants, Int. Math. Research Notices10 (1992), 223-230. Zbl0787.57011
  45. [MMR] J.W. Morgan, T.S. Owka and D. Ruberman - The L2-moduli space and a vanishing theorem for Donaldson polynomial invariants, preprint (1992). 
  46. [MO'G] J.W. Morgan and K.G. O'Grady - Differential topology of complex surfaces (Elliptic surfaces with pg = 1 : smooth classification), L.N. in Math.1545, Springer Verlag (1993). Zbl0789.14037MR1312610
  47. [M] T.S. Owka - A Mayer-Vietoris Principle for Yang-Mills Moduli Spaces, Ph.D. thesis, Berkeley (1989). 
  48. [O'G1] K.G. O'Grady - Algebro-geometric analogues of Donaldson's polynomials, Invent. Math.107 (1992), 351-395. Zbl0769.14008MR1144428
  49. [O'G2] K.G. O'Grady - Donaldson's polynomials for K3-surfaces, J. of Diff. Geom.35 (1992), 415-427. Zbl0735.57011MR1158343
  50. [SS] L.M. Sibner and R.J. Sibner - Classification of Singular Sobolev Connections by Their Holonomy, Commun. Math. Phys.144 (1992), 337-350. Zbl0747.53024MR1152376
  51. [H] J.-C. Sikorav - Homologie associée à une fonctionnelle [d'après A. Floer], Sém. Bourbaki, exp. n° 733, novembre 1990, Astérisque201-202-203 (1991), 115-141. Zbl0754.57011MR1157840
  52. [T] C.H. Taubes - L2-moduli spaces on manifolds with cylindrical ends, Preprint (1990). 
  53. [W] S. Wang - Moduli spaces over manifolds with involutions, Math. Annalen (1993), 119-138. Zbl0788.58012MR1213375
  54. [Wi] E. Witten - Topological Quantum Field Theory, C.M.P. (1988), 353-386. Zbl0656.53078MR953828

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