On positive loops of loose Legendrian embeddings

Guogang Liu

On positive loops of loose Legendrian embeddings

Symplectic Geometry 2017-02-14 v3

Authors: Guogang Liu

Abstract

In this paper, via h-principle we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a new partial order on $\widetilde{Cont}_0(M,\xi)$ and prove that overtwisted contact manifolds are weakly non-orderable.

Keywords

positive loops loose Legendrian embeddings h-principle contractible loops partial order overtwisted contact manifolds weakly non-orderable

Cite

@article{arxiv.1605.07494,
  title  = {On positive loops of loose Legendrian embeddings},
  author = {Guogang Liu},
  journal= {arXiv preprint arXiv:1605.07494},
  year   = {2017}
}

Comments

Simplified proof the main theorem, 14 pages, 6 figures, typos corrected

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