Volume 20, issue 5 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
On the uniqueness of the contact structure approximating a foliation

Thomas Vogel

Geometry & Topology 20 (2016) 2439–2573
Bibliography
1 C Bonatti, S Firmo, Feuilles compactes d’un feuilletage générique en codimension 1, Ann. Sci. École Norm. Sup. 27 (1994) 407 MR1290395
2 J Bowden, Contact perturbations of Reebless foliations are universally tight, preprint (2013) arXiv:1312.2993
3 J Bowden, Contact structures, deformations and taut foliations, Geom. Topol. 20 (2016) 697 MR3493095
4 A Candel, L Conlon, Foliations, I, 23, Amer. Math. Soc. (2000) MR1732868
5 V Colin, Recollement de variétés de contact tendues, Bull. Soc. Math. France 127 (1999) 43 MR1700468
6 V Colin, Stabilité topologique des structures de contact en dimension 3, Duke Math. J. 99 (1999) 329 MR1708018
7 V Colin, Structures de contact tendues sur les variétés toroïdales et approximation de feuilletages sans composante de Reeb, Topology 41 (2002) 1017 MR1923997
8 V Colin, Sur la géométrie des structures de contact en dimension trois : stabilité, flexibilité et finitude, PhD thesis, Université de Nantes (2002)
9 Y Eliashberg, Classification of overtwisted contact structures on 3–manifolds, Invent. Math. 98 (1989) 623 MR1022310
10 Y Eliashberg, Contact 3–manifolds twenty years since J Martinet’s work, Ann. Inst. Fourier (Grenoble) 42 (1992) 165 MR1162559
11 Y Eliashberg, L Polterovich, New applications of Luttinger’s surgery, Comment. Math. Helv. 69 (1994) 512 MR1303225
12 Y M Eliashberg, W P Thurston, Confoliations, 13, Amer. Math. Soc. (1998) MR1483314
13 J B Etnyre, Approximation of foliations by contact structures,
14 H Eynard-Bontemps, Sur deux questions connexes de connexité concernant les feuilletages et leurs holonomies, PhD thesis, École Normale Supérieur de Lyon (2009)
15 H Eynard-Bontemps, On the connectedness of the space of codimension one foliations on a closed 3–manifold, Invent. Math. 204 (2016) 605 MR3489706
16 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
17 D Gabai, Foliations and the topology of 3–manifolds, J. Differential Geom. 18 (1983) 445 MR723813
18 H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008) MR2397738
19 P Ghiggini, S Schönenberger, On the classification of tight contact structures, from: "Topology and geometry of manifolds" (editors G Matić, C McCrory), Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 121 MR2024633
20 E Ghys, V Sergiescu, Stabilité et conjugaison différentiable pour certains feuilletages, Topology 19 (1980) 179 MR572582
21 E Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991) 637 MR1129802
22 E Giroux, Topologie de contact en dimension 3 (autour des travaux de Yakov Eliashberg), from: "Séminaire Bourbaki, 1992–93", Astérisque 216, Société Mathématique de France (1993) 7 MR1246390
23 E Giroux, Une infinité de structures de contact tendues sur une infinité de variétés, Invent. Math. 135 (1999) 789 MR1669264
24 E Giroux, Structures de contact en dimension trois et bifurcations des feuilletages de surfaces, Invent. Math. 141 (2000) 615 MR1779622
25 C Godbillon, Dynamical systems on surfaces, Springer (1983) MR681119
26 R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. 148 (1998) 619 MR1668563
27 S Goodman, Closed leaves in foliated 3–manifolds, Proc. Nat. Acad. Sci. U.S.A. 71 (1974) 4414 MR0350751
28 J Guckenheimer, P Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, 42, Springer (1983) MR709768
29 A Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa 16 (1962) 367 MR0189060
30 P Hartman, Ordinary differential equations, Birkhäuser (1982) MR658490
31 G Hector, Feuilletages en cylindres, from: "Geometry and topology" (editors J Palis, M do Carmo), Lecture Notes in Math. 597, Springer (1977) 252 MR0451260
32 M R Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math. (1979) 5 MR538680
33 M W Hirsch, Stability of compact leaves of foliations, from: "Dynamical systems" (editor M M Peixoto), Academic Press (1973) 135 MR0334236
34 K Honda, On the classification of tight contact structures, I, Geom. Topol. 4 (2000) 309 MR1786111
35 K Honda, On the classification of tight contact structures, II, J. Differential Geom. 55 (2000) 83 MR1849027
36 K Honda, Gluing tight contact structures, Duke Math. J. 115 (2002) 435 MR1940409
37 K Honda, W H Kazez, G Matić, Tight contact structures on fibered hyperbolic 3–manifolds, J. Differential Geom. 64 (2003) 305 MR2029907
38 M Jankins, W D Neumann, Rotation numbers of products of circle homeomorphisms, Math. Ann. 271 (1985) 381 MR787188
39 Y Kanda, The classification of tight contact structures on the 3–torus, Comm. Anal. Geom. 5 (1997) 413 MR1487723
40 P B Kronheimer, T S Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209 MR1474156
41 P B Kronheimer, T S Mrowka, Witten’s conjecture and property P, Geom. Topol. 8 (2004) 295 MR2023280
42 A Larcanché, Topologie locale des espaces de feuilletages en surfaces des variétés fermées de dimension 3, Comment. Math. Helv. 82 (2007) 385 MR2319934
43 Y Mitsumatsu, Anosov flows and non-Stein symplectic manifolds, Ann. Inst. Fourier (Grenoble) 45 (1995) 1407 MR1370752
44 S Morita, T Tsuboi, The Godbillon–Vey class of codimension one foliations without holonomy, Topology 19 (1980) 43 MR559475
45 R Naimi, Foliations transverse to fibers of Seifert manifolds, Comment. Math. Helv. 69 (1994) 155 MR1259611
46 I Nikolaev, E Zhuzhoma, Flows on 2–dimensional manifolds, 1705, Springer (1999) MR1707298
47 S P Novikov, The topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965) 248 MR0200938
48 M M Peixoto, Structural stability on two-dimensional manifolds, Topology 1 (1962) 101 MR0142859
49 C Petronio, A theorem of Eliashberg and Thurston on foliations and contact structures, Scuola Normale Superiore (1997) 64 MR1642484
50 J F Plante, Stability of codimension one foliations by compact leaves, Topology 22 (1983) 173 MR683758
51 H Rosenberg, Foliations by planes, Topology 7 (1968) 131 MR0228011
52 R Sacksteder, Foliations and pseudogroups, Amer. J. Math. 87 (1965) 79 MR0174061
53 W M Schmidt, Diophantine approximation, 785, Springer (1980) MR568710
54 S Sternberg, Local Cn transformations of the real line, Duke Math. J. 24 (1957) 97 MR0102581
55 W Thurston, The theory of foliations of codimension greater than one, Comment. Math. Helv. 49 (1974) 214 MR0370619
56 T Tsuboi, Hyperbolic compact leaves are not C1–stable, from: "Geometric study of foliations" (editors T Mizutani, K Masuda, S Matsumoto, T Inaba, T Tsuboi, Y Mitsumatsu), World Scientific (1994) 437 MR1363741
57 F Varela, Sur une propriété de C0–stabilité des formes de contact en dimension 3, C. R. Acad. Sci. Paris Sér. A-B 280 (1975) MR0372913
58 T Vogel, Rigidity versus flexibility for tight confoliations, Geom. Topol. 15 (2011) 41
59 H Whitney, Geometric integration theory, Princeton Univ. Press (1957) MR0087148