Contact 3-manifolds twenty years since J. Martinet's work

Yakov Eliashberg

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 1-2, page 165-192
  • ISSN: 0373-0956

Abstract

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The paper gives an account of the recent development in 3-dimensional contact geometry. The central result of the paper states that there exists a unique tight contact structure on S 3 . Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on S 3 .

How to cite

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Eliashberg, Yakov. "Contact 3-manifolds twenty years since J. Martinet's work." Annales de l'institut Fourier 42.1-2 (1992): 165-192. <http://eudml.org/doc/74949>.

@article{Eliashberg1992,
abstract = {The paper gives an account of the recent development in 3-dimensional contact geometry. The central result of the paper states that there exists a unique tight contact structure on $S^3$. Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on $S^3$.},
author = {Eliashberg, Yakov},
journal = {Annales de l'institut Fourier},
keywords = {contact geometry; tight contact structure; overtwisted contact structures; 3-manifolds},
language = {eng},
number = {1-2},
pages = {165-192},
publisher = {Association des Annales de l'Institut Fourier},
title = {Contact 3-manifolds twenty years since J. Martinet's work},
url = {http://eudml.org/doc/74949},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Eliashberg, Yakov
TI - Contact 3-manifolds twenty years since J. Martinet's work
JO - Annales de l'institut Fourier
PY - 1992
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 1-2
SP - 165
EP - 192
AB - The paper gives an account of the recent development in 3-dimensional contact geometry. The central result of the paper states that there exists a unique tight contact structure on $S^3$. Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on $S^3$.
LA - eng
KW - contact geometry; tight contact structure; overtwisted contact structures; 3-manifolds
UR - http://eudml.org/doc/74949
ER -

References

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  1. [Be] D. BENNEQUIN, Entrelacements et equations de Pfaff, Astérique, 107-108 (1983), 83-61. Zbl0573.58022MR86e:58070
  2. [Ce] J. CERF, Sur les difféomorphismes de S3 (Г = 0), Lect. Notes in Math., 53 (1968). Zbl0164.24502MR37 #4824
  3. [E1] Y. ELIASHBERG, Classification of overtwisted contact structures on 3-manifolds, Invent. Math., 98 (1989), 623-637. Zbl0684.57012MR90k:53064
  4. [E2] Y. ELIASHBERG, The complexification of contact structures on a 3-manifold, Usp. Math. Nauk., 6(40) (1985), 161-162. Zbl0601.53029
  5. [E3] Y. ELIASHBERG, On symplectic manifolds with some contact properties, J. Diff. Geometry, 33 (1991), 233-238. Zbl0735.53021MR92g:57036
  6. [E4] Y. ELIASHBERG, Filling by holomorphic discs and its applications, London Math. Soc. Lect. Notes Ser., 151 (1991), 45-67. Zbl0731.53036MR93g:53060
  7. [E5] Y. ELIASHBERG, Topological characterization of Stein manifolds of dimension &gt; 2, Int. J. of Math., 1, n°1 (1990), 29-46. Zbl0699.58002MR91k:32012
  8. [E6] Y. ELIASHBERG, New invariants of open symplectic and contact manifolds, J. Amer. Math. Soc., 4 (1991), 513-520. Zbl0733.58011MR92c:58030
  9. [E7] Y. ELIASHBERG, Legendrian and transversal knots in tight contact manifolds, preprint, 1991. 
  10. [EG] Y. ELIASHBERG and M. GROMOV, Convex symplectic manifolds, Proc. of Symposia in Pure Math., 52 (1991), part 2, 135-162. Zbl0742.53010MR93f:58073
  11. [Gi] E. GIROUX, Convexité en topologie de contact, to appear in Comm. Math. Helvet., 1991. Zbl0766.53028MR93b:57029
  12. [Gro] M. GROMOV, Pseudoholomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347. Zbl0592.53025MR87j:53053
  13. [HE] V. HARLAMOV and Y. ELIASHBERG, On the number of complex points of a real surface in a complex surface, Proc. LITC-82, (1982), 143-148. Zbl0609.32016
  14. [Lu] R. LUTZ, Structures de contact sur les fibre's principaux en cercles de dimension 3, Ann. Inst. Fourier, 27-3 (1977), 1-15. Zbl0328.53024MR57 #17668
  15. [Ma] J. MARTINET, Formes de contact sur les variétés de dimension 3, Lect. Notes in Math, 209 (1971), 142-163. Zbl0215.23003MR50 #3263
  16. [McD] D. MCDUFF, The structure of rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc., 3, n°1 (1990), 679-712. Zbl0723.53019MR91k:58042

Citations in EuDML Documents

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  1. Burak Ozbagci, On the Heegaard genus of contact 3-manifolds
  2. Thilo Kuessner, An invariant of nonpositively curved contact manifolds
  3. M. E. A. Hadjar, Sur un problème d'existence relatif de formes de contact invariantes en dimension trois
  4. Vincent Colin, Chirurgies de Dehn admissibles dans les variétés de contact tendues
  5. Vincent Colin, Recollement de variétés de contact tendues
  6. Yoshihiko Mitsumatsu, Anosov flows and non-Stein symplectic manifolds
  7. Vincent Colin, Sur la torsion des structures de contact tendues
  8. Emmanuel Giroux, Une structure de contact, même tendue, est plus ou moins tordue
  9. Vincent Colin, Emmanuel Giroux, Ko Honda, Finitude homotopique et isotopique des structures de contact tendues
  10. François Laudenbach, Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3

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