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Positive Legendrian isotopies and Floer theory. (Isotopies legendriennes positives et théorie de Floer.) (English. French summary) Zbl 1426.53092

Summary: 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 filled by a Liouville domain with non-zero symplectic homology are strongly orderable in the sense of G. Liu [“On positive loops of loose Legendrian embeddings”, Preprint, arXiv:1605.07494].

MSC:

53D42 Symplectic field theory; contact homology
57R58 Floer homology
53D10 Contact manifolds (general theory)
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