Applications of convex integration to symplectic and contact geometry

Dusa McDuff

Annales de l'institut Fourier (1987)

  • Volume: 37, Issue: 1, page 107-133
  • ISSN: 0373-0956

Abstract

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We apply Gromov’s method of convex integration to problems related to the existence and uniqueness of symplectic and contact structures

How to cite

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McDuff, Dusa. "Applications of convex integration to symplectic and contact geometry." Annales de l'institut Fourier 37.1 (1987): 107-133. <http://eudml.org/doc/74740>.

@article{McDuff1987,
abstract = {We apply Gromov’s method of convex integration to problems related to the existence and uniqueness of symplectic and contact structures},
author = {McDuff, Dusa},
journal = {Annales de l'institut Fourier},
keywords = {convex integration; symplectic geometry; contact geometry; foliations},
language = {eng},
number = {1},
pages = {107-133},
publisher = {Association des Annales de l'Institut Fourier},
title = {Applications of convex integration to symplectic and contact geometry},
url = {http://eudml.org/doc/74740},
volume = {37},
year = {1987},
}

TY - JOUR
AU - McDuff, Dusa
TI - Applications of convex integration to symplectic and contact geometry
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 1
SP - 107
EP - 133
AB - We apply Gromov’s method of convex integration to problems related to the existence and uniqueness of symplectic and contact structures
LA - eng
KW - convex integration; symplectic geometry; contact geometry; foliations
UR - http://eudml.org/doc/74740
ER -

References

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  1. [B] D. BENNEQUIN, Entrelacements et équations de Pfaff, Astérisque, 107-108 (1983), 87-161. Zbl0573.58022MR86e:58070
  2. [C] E. CARTAN, Les systèmes différentiels extérieurs et leurs applications géométriques, Herman, Paris (1945). Zbl0063.00734MR7,520d
  3. [E] J. ELIASHBERG, Rigidity of symplectic and contact structures, Preprint, 1981. 
  4. [GS] R. GREENE and K. SHIOHAMA, Diffeomorphisms and volume-preserving embeddings of non-compact manifolds, TAMS, 225 (1979), 403-414. Zbl0418.58002MR80k:58031
  5. [G1] M. GROMOV, Stable mappings of foliations into manifolds, Izv. Akad. Nauk SSR, Mat, 33 (1969), 707-734. Zbl0197.20404
  6. [G2] M. GROMOV, Convex integration of differential relations I, Math USSR Izv., 7 (1973), 329-343. Zbl0281.58004MR54 #1323
  7. [G3] M. GROMOV, Partial Differential Relations, Springer Verlag, to appear. Zbl0651.53001
  8. [G4] M. GROMOV, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347. Zbl0592.53025MR87j:53053
  9. [H1] A. HAEFLIGER, Feuilletages sur les variétés ouvertes, Topology, 9 (1970), 183-194. Zbl0196.26901MR41 #7709
  10. [H2] A. HAEFLIGER, Homotopy and integrability, Manifolds-Amsterdam, Springer Lecture Notes # 197 (1971) 133-163. Zbl0215.52403MR44 #2251
  11. [H3] A. HAEFLIGER, Lectures on the theorem of Gromov, Springer Lecture Notes # 209, (1971), 128-141. Zbl0222.57020MR48 #12560
  12. [M] J. MARTINET, Formes de contact sur les variétés de dimension 3, Springer Lecture Notes # 209, (1971), 128-163. Zbl0215.23003MR50 #3263
  13. [MD1] D. MCDUFF, On groups of volume-preserving diffeomorphisms and foliations with transverse volume form, Proc. London Math. Soc., 43 (1981), 295-320. Zbl0411.57028MR83g:58007
  14. [MD2] D. MCDUFF, Local homology of groups of volume-preserving diffeomorphisms, I, Ann. Sci. Ec. Norm. Sup., 15 (1982), 609-648. Zbl0577.58005MR85i:58028
  15. [MD3] D. MCDUFF, Some canonical cohomology classes on groups of volume-preserving diffeomorphisms, TAMS, 275 (1983), 345-356. Zbl0522.57029MR84h:58154
  16. [MD4] D. MCDUFF, Examples of simply connected symplectic non-Kählerian manifolds, J. Diff. Geom., 20 (1984), 27. Zbl0567.53031MR86c:57036
  17. [MD5] D. MCDUFF, Examples of symplectic structures, to appear in Invent. Math. Zbl0625.53040
  18. [Me] C. MECKERT, Formes de contact sur la somme connexe de deux variétés de contact, Ann. Inst. Fourier, Grenoble, 32-3 (1982), 251-260. Zbl0471.58001MR84f:53031
  19. [Mo] J. MOSER, On the volume elements on a manifolds, TAMS, 120 (1965), 286-294. Zbl0141.19407MR32 #409
  20. [Sp] D. SPRING, Convex integration of non-linear system of partial differential equations, Ann. Inst. Fourier, Grenoble, 33-3 (1983) 121-177. Zbl0507.35019MR85i:58126
  21. [S] D. SULLIVAN, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math., 36 (1976), 225-255. Zbl0335.57015MR55 #6440
  22. [To] C. THOMAS, A classifying space for the contact pseudogroup, Mathematika, 25 (1978), 191-201. Zbl0404.53031MR80i:57021
  23. [T] W. THURSTON, Some simple examples of symplectic manifolds, Proc. AMS, 55 (1976), 467-468. Zbl0324.53031MR53 #6578
  24. [TW] W. THURSTON and H. WINKELNKEMPER, On the existence of contact forms, Proc. AMS, 52 (1975), 345-347. Zbl0312.53028MR51 #11561
  25. [V] C. VITERBO, A Proof of Weinstein's conjecture in R2n, preprint, 1986. Zbl0631.58013
  26. [W] A. WEINSTEIN, On the hypotheses of Rabinowitz's periodic orbit theorems, J. Diff. Eq., 33 (1979), 353-358. Zbl0388.58020MR81a:58030b

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