Tight contact structures and taut foliations
Geometry & topology, Tome 4 (2000) no. 1, pp. 219-242.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.

DOI : 10.2140/gt.2000.4.219
Keywords: tight, contact structure, taut foliation

Honda, Ko 1 ; Kazez, William H 1 ; Matić, Gordana 1

1 Mathematics Department, University of Georgia, Athens, Georgia 30602, USA
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Honda, Ko; Kazez, William H; Matić, Gordana. Tight contact structures and taut foliations. Geometry & topology, Tome 4 (2000) no. 1, pp. 219-242. doi : 10.2140/gt.2000.4.219. http://geodesic.mathdoc.fr/articles/10.2140/gt.2000.4.219/

[1] D Bennequin, Entrelacements et équations de Pfaff, from: "Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982)", Astérisque 107, Soc. Math. France (1983) 87

[2] V Colin, Chirurgies d'indice un et isotopies de sphères dans les variétés de contact tendues, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 659

[3] V Colin, Recollement de variétés de contact tendues, Bull. Soc. Math. France 127 (1999) 43

[4] Y Eliashberg, Classification of overtwisted contact structures on 3–manifolds, Invent. Math. 98 (1989) 623

[5] Y Eliashberg, Topological characterization of Stein manifolds of dimension $\gt 2$, Internat. J. Math. 1 (1990) 29

[6] Y Eliashberg, Filling by holomorphic discs and its applications, from: "Geometry of low-dimensional manifolds, 2 (Durham, 1989)", London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 45

[7] Y Eliashberg, Contact 3–manifolds twenty years since J Martinet's work, Ann. Inst. Fourier (Grenoble) 42 (1992) 165

[8] Y Eliashberg, Unique holomorphically fillable contact structure on the 3–torus, Internat. Math. Res. Notices (1996) 77

[9] J B Etnyre, K Honda, On the nonexistence of tight contact structures, Ann. of Math. $(2)$ 153 (2001) 749

[10] Y M Eliashberg, W P Thurston, Confoliations, University Lecture Series 13, American Mathematical Society (1998)

[11] D Gabai, Foliations and the topology of 3–manifolds, J. Differential Geom. 18 (1983) 445

[12] E Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991) 637

[13] E Giroux, Une structure de contact, même tendue, est plus ou moins tordue, Ann. Sci. École Norm. Sup. $(4)$ 27 (1994) 697

[14] E Giroux, Structures de contact en dimension trois et bifurcations des feuilletages de surfaces, Invent. Math. 141 (2000) 615

[15] R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. $(2)$ 148 (1998) 619

[16] M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307

[17] K Honda, On the classification of tight contact structures I, Geom. Topol. 4 (2000) 309

[18] K Honda, Gluing tight contact structures, Duke Math. J. 115 (2002) 435

[19] K Honda, W H Kazez, G Matić, in preparation

[20] W Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics 43, American Mathematical Society (1980)

[21] Y Kanda, The classification of tight contact structures on the 3–torus, Comm. Anal. Geom. 5 (1997) 413

[22] Y Kanda, On the Thurston–Bennequin invariant of Legendrian knots and nonexactness of Bennequin's inequality, Invent. Math. 133 (1998) 227

[23] P Lisca, Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998) 103

[24] P Lisca, G Matić, Stein 4–manifolds with boundary and contact structures, Topology Appl. 88 (1998) 55

[25] S Makar-Limanov, Morse surgeries of index 0 on tight manifolds, preprint (1997)

[26] J Martinet, Formes de contact sur les variétés de dimension 3, from: "Proceedings of Liverpool Singularities Symposium II (1969/1970)", Lecture Notes in Math. 209, Springer (1971) 142

[27] S P Novikov, The topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965) 248

[28] W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 59 (1986) 99

[29] I Torisu, Convex contact structures and fibered links in 3–manifolds, Internat. Math. Res. Notices (2000) 441

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