×

zbMATH — the first resource for mathematics

Even a tight contact structure, is more or less twisted. (Une structure de contact, même tendue, est plus ou moins tordue.) (French) Zbl 0819.53018
Using the papers of Y. Eliashberg [Ann. Inst. Fourier 42, No. 1-2, 165-192 (1992; Zbl 0756.53017)] and of J.-C. Sikorav [ Mém. Soc. Math. Fr., Nouv. Sér. 46, 151-167 (1991; Zbl 0751.58010)] the author proves the existence of non isometric tight contact structures on \(T^ 3\) and that all Lagrangian incompressible embedded tori in \(\mathbb{T}^ 2 \times (\mathbb{R}^ 2 \setminus \{0\})\) are homotopic.
Reviewer: P.Stavre (Craiova)

MSC:
53D35 Global theory of symplectic and contact manifolds
57R17 Symplectic and contact topology in high or arbitrary dimension
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] D. BENNEQUIN , Entrelacements et équations de Pfaff (Astérisque, Vol. 107-108, 1983 , p. 83-161). MR 86e:58070 | Zbl 0573.58022 · Zbl 0573.58022
[2] Y. ELIASHBERG , Classification of over-twisted contact structures on 3-manifolds (Inv. Math., Vol. 98, 1989 , p. 623-637). MR 90k:53064 | Zbl 0684.57012 · Zbl 0684.57012 · doi:10.1007/BF01393840 · eudml:143746
[3] Y. ELIASHBERG , Contact 3-manifolds, twenty years since J. Martinet’s work (Ann. Inst. Fourier, Vol. 42, 1992 , p. 165-192). Numdam | MR 93k:57029 | Zbl 0756.53017 · Zbl 0756.53017 · doi:10.5802/aif.1288 · numdam:AIF_1992__42_1-2_165_0 · eudml:74949
[4] Y. ELIASHBERG , New invariants of open symplectic and contact manifolds (J. Amer. Math. Soc., Vol. 4, 1991 , p. 513-520). MR 92c:58030 | Zbl 0733.58011 · Zbl 0733.58011 · doi:10.2307/2939267
[5] Y. ELIASHBERG , Filling by holomorphic discs and its applications (London Math. Soc. Lect. Notes Ser., 151, 1991 , p. 45-67). MR 93g:53060 | Zbl 0731.53036 · Zbl 0731.53036
[6] Y. ELIASHBERG , communication orale privée sur des travaux récents de W. THURSTON (mai 1992 ).
[7] E. GIROUX , Convexité en topologie de contact (Comment. Math. Helvetici, Vol. 66, 1991 , p. 637-677). MR 93b:57029 | Zbl 0766.53028 · Zbl 0766.53028 · doi:10.1007/BF02566670 · eudml:140253
[8] M. GROMOV , Pseudo-holomorphic curves in symplectic manifolds (Inv. Math., Vol. 82, 1985 , p. 307-347). MR 87j:53053 | Zbl 0592.53025 · Zbl 0592.53025 · doi:10.1007/BF01388806 · eudml:143289
[9] F. LALONDE et J.-C. SIKORAV , Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents (Comment. Math. Helvetici, Vol. 66, 1991 , p. 18-33). MR 92f:58060 | Zbl 0759.53022 · Zbl 0759.53022 · doi:10.1007/BF02566634 · eudml:140221
[10] J.-C. SIKORAV , Quelques propriétés des plongements lagrangiens (Suppl. Bull. Soc. Math. France, Mem. No 46, Vol. 119, 1991 , p. 151-167). Numdam | MR 93f:57033 | Zbl 0751.58010 · Zbl 0751.58010 · numdam:MSMF_1991_2_46__151_0 · eudml:94891
[11] J.-C. SIKORAV , Rigidité symplectique dans le cotangent de Tn (Duke Math. J., Vol. 59, 1989 , p. 227-231). Article | MR 91e:58063 | Zbl 0697.53035 · Zbl 0697.53035 · doi:10.1215/S0012-7094-89-05935-8 · minidml.mathdoc.fr
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.