Geometry & Topology Volume 20, issue 5 (2016)

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On the uniqueness of the contact structure approximating a foliation

Thomas Vogel

Geometry & Topology 20 (2016) 2439–2573

DOI: 10.2140/gt.2016.20.2439

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