Geometry & Topology Volume 25, issue 2 (2021)

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Quasicomplementary foliations and the Mather–Thurston theorem

Gaël Meigniez

Geometry & Topology 25 (2021) 643–710

DOI: 10.2140/gt.2021.25.643

Bibliography

1	M F Atiyah, F Hirzebruch, Vector bundles and homogeneous spaces, from: "Proceedings of symposia in pure mathematics, III : Differential geometry" (editor C B Allendoerfer), Amer. Math. Soc. (1961) 7 MR0139181
2	C Camacho, A Lins Neto, Geometric theory of foliations, Birkhäuser (1985) MR824240
3	A Candel, L Conlon, Foliations, I, 23, Amer. Math. Soc. (2000) MR1732868
4	Y Eliashberg, S Galatius, N Mishachev, Madsen–Weiss for geometrically minded topologists, Geom. Topol. 15 (2011) 411 MR2776850
5	Y Eliashberg, N M Mishachev, Wrinkling of smooth mappings and its applications, I, Invent. Math. 130 (1997) 345 MR1474161
6	Y Eliashberg, N M Mishachev, Wrinkling of smooth mappings, III : Foliations of codimension greater than one, Topol. Methods Nonlinear Anal. 11 (1998) 321 MR1659446
7	Y Eliashberg, N Mishachev, Introduction to the h–principle, 48, Amer. Math. Soc. (2002) MR1909245
8	D B A Epstein, The simplicity of certain groups of homeomorphisms, Compos. Math. 22 (1970) 165 MR267589
9	D B Fuchs, Quillenization and bordism, Funktsional. Anal. i Prilozhen. 8 (1974) 36 MR0343301
10	M L Gromov, Stable mappings of foliations into manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969) 707 MR0263103
11	M Gromov, Partial differential relations, 9, Springer (1986) MR864505
12	A Haefliger, Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv. 32 (1958) 248 MR100269
13	A Haefliger, Espaces universels pour les feuilletages, from: "Colloque de topologie différentielle" (editors C Godbillon, H W Rosenberg), Univ. Montpellier (1969) 11 MR0256412
14	A Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970) 183 MR263104
15	A Haefliger, Homotopy and integrability, from: "Manifolds : Amsterdam" (editor N H Kuiper), Lecture Notes in Math. 197, Springer (1971) 133 MR0285027
16	M W Hirsch, B Mazur, Smoothings of piecewise linear manifolds, 80, Princeton Univ. Press (1974) MR0415630
17	J F P Hudson, Piecewise linear topology, Benjamin (1969) MR0248844
18	A Kupers, Three applications of delooping to h–principles, Geom. Dedicata 202 (2019) 103 MR4001810
19	F Laudenbach, Transversalité, courants et théorie de Morse, Éd. l’École Polytech. (2012) MR3088239
20	F Laudenbach, G Meigniez, Haefliger structures and symplectic/contact structures, J. Éc. Polytech. Math. 3 (2016) 1 MR3477863
21	J N Mather, Integrability in codimension 1, Comment. Math. Helv. 48 (1973) 195 MR356085
22	J N Mather, Loops and foliations, from: "Manifolds : Tokyo" (editor A Hattori), Univ. Tokyo Press (1975) 175 MR0368032
23	J N Mather, On the homology of Haefliger’s classifying space, from: "Differential topology" (editor V Villani), Liguori Editore (1979) 71 MR660655
24	D McDuff, Foliations and monoids of embeddings, from: "Geometric topology" (editor J C Cantrell), Academic (1979) 429 MR537744
25	D McDuff, The homology of some groups of diffeomorphisms, Comment. Math. Helv. 55 (1980) 97 MR569248
26	G Meigniez, Realizing compactly generated pseudo-groups of dimension one, J. Math. Soc. Japan 68 (2016) 1747 MR3564450
27	G Meigniez, Regularization and minimization of codimension-one Haefliger structures, J. Differential Geom. 107 (2017) 157 MR3698236
28	J Milnor, Lectures on the h–cobordism theorem, Princeton Univ. Press (1965) MR0190942
29	J Milnor, Foliations and foliated vector bundles, from: "Collected papers of John Milnor, IV : Homotopy, homology and manifolds" (editor J McCleary), Amer. Math. Soc. (2009) 279 MR2590677
30	Y Mitsumatsu, E Vogt, Thurston’s h–principle for 2–dimensional foliations of codimension greater than one, from: "Geometry, dynamics, and foliations" (editors T Asuke, S Matsumoto, Y Mitsumatsu), Adv. Stud. Pure Math. 72, Math. Soc. Japan (2017) 181 MR3726709
31	S Nariman, Stable homology of surface diffeomorphism groups made discrete, Geom. Topol. 21 (2017) 3047 MR3687114
32	A Phillips, Smooth maps transverse to a foliation, Bull. Amer. Math. Soc. 76 (1970) 792 MR263106
33	V Poenaru, On regular homotopy in codimension 1, Ann. of Math. 83 (1966) 257 MR192507
34	G Segal, Classifying spaces related to foliations, Topology 17 (1978) 367 MR516216
35	W Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974) 304 MR339267
36	W Thurston, The theory of foliations of codimension greater than one, Comment. Math. Helv. 49 (1974) 214 MR370619
37	W P Thurston, Existence of codimension-one foliations, Ann. of Math. 104 (1976) 249 MR425985
38	T Tsuboi, On the foliated products of class C¹, Ann. of Math. 130 (1989) 227 MR1014925
39	H Whitney, Geometric integration theory, Princeton Univ. Press (1957) MR0087148