Positive isotopies of Legendrian submanifolds and applications

Vincent Colin; Emmanuel Ferrand; Petya Pushkar

Positive isotopies of Legendrian submanifolds and applications

Symplectic Geometry 2010-05-02 v1

Authors: Vincent Colin , Emmanuel Ferrand , Petya Pushkar

Abstract

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.

Keywords

positive isotopies Legendrian submanifolds contact manifold Legendrian embeddings one-jets tight contact 3-manifold

Cite

@article{arxiv.1004.5263,
  title  = {Positive isotopies of Legendrian submanifolds and applications},
  author = {Vincent Colin and Emmanuel Ferrand and Petya Pushkar},
  journal= {arXiv preprint arXiv:1004.5263},
  year   = {2010}
}

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