Positive Legendrian isotopies and Floer Theory

Abstract

Positive loops of Legendrian embeddings are examined from the point of view of Floer homology of Lagrangian cobordisms. This leads to new obstructions to the existence of a positive loop containing a given Legendrian, expressed in terms of the Legendrian contact homology of the Legendrian submanifold. As applications, old and new examples of orderable contact manifolds are obtained and discussed. We also show that contact manifolds admitting a filling of a Liouville domain with non-zero symplectic homology is strongly orderable in the sense of Liu.

43 pages. v2: more details, mainly in Section 5. Changes in introduction, added some references and Theorem 1.19. v3: minor corrections, v4: update in the bibliography and change the references accordingly. To appear at "Annales de l'Institut Fourier"