La conjecture de Weinstein en dimension 3 [d'après C. H. Taubes]

Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Exposé no. 1002, 25 p.

MR 2648677 | Zbl 1220.53005

@incollection{AST_2010__332__135_0,
     author = {Auroux, Denis},
     title = {La conjecture de Weinstein en dimension 3 [d'apr\`es C. H. Taubes]},
     booktitle = {S\'eminaire Bourbaki : volume 2008/2009 expos\'es 997-1011  - Avec table par noms d'auteurs de 1848/49 \`a 2008/09},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:1002},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {332},
     year = {2010},
     zbl = {1220.53005},
     mrnumber = {2648677},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2010__332__135_0/}
}

Auroux, Denis. La conjecture de Weinstein en dimension 3 [d'après C. H. Taubes], dans Séminaire Bourbaki : volume 2008/2009 exposés 997-1011  - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Exposé no. 1002, 25 p. http://archive.numdam.org/item/AST_2010__332__135_0/

Bibliographie

[1] C. Abbas, K. Cieliebak & H. Hofer - The Weinstein conjecture for planar contact structures in dimension three, Comment. Math. Helv. 80 (2005), p. 771-793. | Article | MR 2182700 | Zbl 1098.53063

[2] D. T. Gay - Four-dimensional symplectic cobordisms containing three-handles, Geom. Topol. 10 (2006), p. 1749-1759. | Article | MR 2284049 | Zbl 1129.53061

[3] H. Hofer - Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993), p. 515- 563. | Article | EuDML 144157 | MR 1244912 | Zbl 0797.58023

[4] M. Hutchings - An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. (JEMS) 4 (2002), p. 313-361. | Article | EuDML 277717 | MR 1941088 | Zbl 1017.58005

[5] M. Hutchings & M. Sullivan - Rounding corners of polygons and the embedded contact homology of $T^{3}$ , Geom. Topol. 10 (2006), p. 169-266. | Article | EuDML 126791 | MR 2207793 | Zbl 1101.53053

[6] M. Hutchings & C. H. Taubes - Gluing pseudoholomorphic curves along branched covered cylinders. I, J. Symplectic Geom. 5 (2007), p. 43-137. | Article | MR 2371184 | Zbl 1157.53047

[7] M. Hutchings & C. H. Taubes, The Weinstein conjecture for stable Hamiltonian structures, Geom. Topol. 13 (2009), p. 901-941. | Article | MR 2470966 | Zbl 1169.53065

[8] D. Kotschick - The Seiberg-Witten invariants of symplectic four-manifolds (after C. H. Taubes), Séminaire Bourbaki, vol. 1995/96, exposé n° 812, Astérisque 241 (1997), p. 195-220. | EuDML 110214 | Numdam | MR 1472540 | Zbl 0882.57026

[9] P. Kronheimer & T. Mrowka - Monopoles and three-manifolds, New Mathematical Monographs, vol. 10, Cambridge Univ. Press, 2007. | MR 2388043 | Zbl 1158.57002

[10] F. Laudenbach - Orbites périodiques et courbes pseudo-holomorphes, application à la conjecture de Weinstein en dimension 3 (d'après H. Hofer et al.), Séminaire Bourbaki, vol. 1993/94, exposé n° 786, Astérisque 227 (1995), p. 309-333. | EuDML 110189 | Numdam | MR 1321652 | Zbl 0853.57013

[11] Y.-G. Oh - Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, in The breadth of symplectic and Poisson geometry, Progr. Math., vol. 232, Birkhäuser, 2005, p. 525-570. | MR 2103018 | Zbl 1084.53076

[12] P. H. Rabinowitz - Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), p. 157-184. | Article | MR 467823 | Zbl 0358.70014

[13] M. Schwarz - On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000), p. 419-461. | Article | MR 1755825 | Zbl 1023.57020

[14] C. H. Taubes - The Seiberg-Witten and Gromov invariants, Math. Res. Lett. 2 (1995), p. 221-238. | Article | MR 1324704 | Zbl 0854.57020

[15] C. H. Taubes, $SW \Rightarrow Gr$ : from the Seiberg-Witten equations to pseudo-holomorphic curves, J. Amer. Math. Soc. 9 (1996), p. 845-918. | Article | MR 1362874 | Zbl 0867.53025

[16] C. H. Taubes, The geometry of the Seiberg-Witten invariants, in Surveys in differential geometry, Vol. III (Cambridge, MA, 1996), Int. Press, Boston, MA, 1998, p. 299-339. | MR 1677891 | Zbl 0956.57019

[17] C. H. Taubes, $Gr ⟹ SW$ : from pseudo-holomorphic curves to Seiberg-Witten solutions, J. Differential Geom. 51 (1999), p. 203-334. | Article | MR 1728301 | Zbl 1036.53066

[18] C. H. Taubes, The Seiberg-Witten equations and the Weinstein conjecture, Geom. Topol. 11 (2007), p. 2117-2202. | Article | MR 2350473 | Zbl 1135.57015

[19] C. H. Taubes, The Seiberg-Witten equations and the Weinstein conjecture. II. More closed integral curves of the Reeb vector field, Geom. Topol. 13 (2009), p. 1337-1417. | Article | MR 2496048 | Zbl 1200.57018

[20] C. H. Taubes, Embedded contact homology and Seiberg-Witten Floer cohomology I, prépublication arXiv:0811.3985. | MR 2746724 | Zbl 1275.57037

[21] C. Viterbo - A proof of Weinstein's conjecture in $𝐑^{2 n}$ , Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), p. 337-356. | Article | EuDML 78135 | Numdam | MR 917741 | Zbl 0631.58013

[22] A. Weinstein - On the hypotheses of Rabinowitz' periodic orbit theorems, J. Differential Equations 33 (1979), p. 353-358. | Article | MR 543704 | Zbl 0388.58020