Existence h-principle for Engel structures

被引：14

作者：

Casals, Roger ^{[1
]}

Luis Perez, Jose ^{[2
]}

del Pino, Alvaro ^{[2
]}

Presas, Francisco ^{[2
]}

机构：

[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] CSIC, UAM, UC3M, UCM,Inst Ciencias Matemat, C Nicolas Cabrera 13-15, E-28049 Madrid, Spain

来源：

INVENTIONES MATHEMATICAE | 2017年 / 210卷 / 02期

关键词：

OVERTWISTED CONTACT STRUCTURES; CLASSIFICATION; FOLIATIONS;

D O I：

10.1007/s00222-017-0732-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we prove that the inclusion of the space of Engel structures of a smooth 4-manifold into the space of full flags of its tangent bundle induces surjections in all homotopy groups. In particular, we construct Engel structures representing any given full flag.

引用

页码：417 / 451

页数：35

共 19 条

[1]

[Anonymous], 2002, GRADUATE STUDIES MAT

[2] ROUND HANDLES AND NON-SINGULAR MORSE-SMALE FLOWS [J].

ASIMOV, D .

ANNALS OF MATHEMATICS, 1975, 102 (01) :41-54

[3] Existence and classification of overtwisted contact structures in all dimensions [J].

Borman, Matthew Strom ;

Eliashberg, Yakov ;

Murphy, Emmy .

ACTA MATHEMATICA, 2015, 215 (02) :281-361

[4]

Cartan E., 1901, B SOC MATH FRANCE, V29, P118, DOI 10.24033/bsmf.639

[5]

Cartan E., 1924, Bulletin de la Socit Mathmatique de France, V52, P205, DOI [10.24033/bsmf.1053, DOI 10.24033/BSMF.1053]

[6] Almost contact 5-manifolds are contact [J].

Casals, Roger ;

Pancholi, Dishant M. ;

Presas, Francisco .

ANNALS OF MATHEMATICS, 2015, 182 (02) :429-490

[7] CONTACT 3-MANIFOLDS 20 YEARS SINCE MARTINET,J. WORK [J].

ELIASHBERG, Y .

ANNALES DE L INSTITUT FOURIER, 1992, 42 (1-2) :165-192

[8] CLASSIFICATION OF OVERTWISTED CONTACT STRUCTURES ON 3-MANIFOLDS [J].

ELIASHBERG, Y .

INVENTIONES MATHEMATICAE, 1989, 98 (03) :623-637

[9] CALCULATION OF CONTACT AND SYMPLECTIC COBORDISM-GROUPS [J].

GINZBURG, VL .

TOPOLOGY, 1992, 31 (04) :767-773

[10]

Golubev A, 1997, INT MATH RES NOTICES, V1997, P523

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