Positive isotopies of Legendrian submanifolds and applications

Vincent Colin (1) , Emmanuel Ferrand (2) , Petya Pushkar (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IMJ - Institut de Mathématiques de Jussieu
3 ULB - Université libre de Bruxelles

We show that there is no positive loop inside the component of a fiber in the space of Legendrian embeddings in the contact manifold $ST^*M$, provided that the universal cover of $M$ is $\RM^n$. We consider some related results in the space of one-jets of functions on a compact manifold. We give an application to the positive isotopies in homogeneous neighborhoods of surfaces in a tight contact 3-manifold.

Mots clés: Contact structure; Legendrian submanifolds; positive isotopies; Morse theory

Domaines: Géométrie symplectique [math.SG]

Vincent Colin, Emmanuel Ferrand, Petya Pushkar. Positive isotopies of Legendrian submanifolds and applications. International Mathematics Research Notices, 2017, 20, pp.6231-6254. ⟨hal-00463048⟩