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Positive isotopies of Legendrian submanifolds and applications

arxiv.org. math. Cornell University, 2010. No. 1004.5263v1.
Pushkar P. E., Ferrand E., Colin V.

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 Rn. 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.