no. 1
Differential Topology
A construction of Engel structures
[Une construction des structures d'Engel]

Présenté par : Étienne Ghys

Vogel, Thomas1
1 Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresien Strasse 39, 80333 München, Germany
Comptes Rendus. Mathématique, Tome 340 (2005) no. 1, pp. 43-48.

Toute variété de dimension 4 dont le fibré tangent est trivial admet une structure d'Engel.

Every 4-manifold with trivial tangent bundle admits an Engel structure.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.11.011
Vogel, Thomas 1

1 Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresien Strasse 39, 80333 München, Germany 
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Vogel, Thomas. A construction of Engel structures. Comptes Rendus. Mathématique, Tome 340 (2005) no. 1, pp. 43-48. doi : 10.1016/j.crma.2004.11.011. http://www.numdam.org/articles/10.1016/j.crma.2004.11.011/

[1] Asimov, D. Round handles and non-singular Morse–Smale flows, Ann. Math., Volume 102 (1975) no. 2, pp. 41-54

[2] Eliashberg, Y.; Mishachev, N. Introduction to the h-Principle, Grad. Stud. Math., vol. 48, American Mathematical Society, 2002

[3] Engel, F. Zur Invariantentheorie der Systeme Pfaff'scher Gleichungen, Leipziger Ber., Volume 41 (1889), pp. 157-176

[4] H.J. Geiges, Review of [6], http://www.ams.org/mathscinet, MR 2001h:53127

[5] Kazarian, M.; Montgomery, R.; Shapiro, B. Characteristic classes for the degenerations of two-plane fields in four dimensions, Pacific J. Math., Volume 179 (1997) no. 2, pp. 355-370

[6] Montgomery, R. Engel deformations and contact structures, Northern Calif. Sympl. Geom. Sem. 103–117, Amer. Math. Soc. Transl. Ser. 2, vol. 196, 1999

[7] Morgan, J.W. Nonsingular Morse–Smale flows on 3-dimensional manifolds, Topology, Volume 18 (1979) no. 1, pp. 41-53

[8] T. Vogel, Existence of Engel structures, thesis, Ludwig-Maximilians-Universität München, 2004

[9] T. Vogel, Existence of Engel structures, preprint, submitted for publication

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