We define an invariant of contact structures and foliations (on Riemannian manifolds of nonpositive sectional curvature) which is upper semi-continuous with respect to deformations and thus gives an obstruction to the topology of foliations which can be approximated by isotopies of a given contact structure.
@article{bwmeta1.element.doi-10_2478_s11533-010-0084-6,
author = {Thilo Kuessner},
title = {An invariant of nonpositively curved contact manifolds},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {173-183},
zbl = {1209.53066},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0084-6}
}
Thilo Kuessner. An invariant of nonpositively curved contact manifolds. Open Mathematics, Tome 9 (2011) pp. 173-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0084-6/
[1] Benedetti R., Petronio C., Lectures on Hyperbolic Geometry, Universitext, Springer, Berlin, 1992 | Zbl 0768.51018
[2] Calegari D., The Gromov norm and foliations, Geom. Funct. Anal., 2000, 10(6), 1423–1447 http://dx.doi.org/10.1007/PL00001655 | Zbl 0974.57015
[3] Eliashberg Y., Contact 3-manifolds twenty years since J.Martinet's work, Ann. Inst. Fourier (Grenoble), 1992, 42(1–2), 165–192
[4] Eliashberg Y., Thurston W.P., Confoliations, Univ. Lecture Ser., 13, AMS, Providence, 1998
[5] Geiges, H., An Introduction to Contact Topology, Cambridge Stud. Adv. Math., 109, Cambridge University Press, Cambridge, 2008 | Zbl 1153.53002
[6] Giroux E., Structures de contact sur les variétés fibrées en cercles audessus d'une surface, Comment. Math. Helv., 2001, 76(2), 218–262 http://dx.doi.org/10.1007/PL00000378 | Zbl 0988.57015
[7] Gromov M., Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math., 1982, 56, 5–99