On positive loops of loose Legendrian embeddings

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.

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

References in corpus (3)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Geometric criteria for overtwistedness
• On the non-existence of small positive loops of contactomorphisms on overtwisted contact manifolds