Positive Legendrian isotopies and Floer theory
Annales de l'Institut Fourier, Volume 69 (2019) no. 4, p. 1679-1737

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 Liu.

On étudie les lacets positifs de plongements legendriens du point de vue de l’homologie de Floer pour les cobordismes lagrangiens. On obtient ainsi de nouvelles obstructions à l’existence d’un lacet positif contenant une sous-variété legendrienne donnée, exprimées à l’aide de son homologie de contact legendrienne. On applique ensuite ces obstructions pour revisiter d’anciens et donner de nouveaux exemples de variétés de contact ordonnables. On démontre également qu’une variété de contact remplissable par un domaine de Liouville dont l’homologie symplectique est non triviale est fortement ordonnable au sens de Liu.

Received : 2018-02-23
Accepted : 2018-06-12
Published online : 2019-09-16
DOI : https://doi.org/10.5802/aif.3279
Classification:  53D42,  57R58,  53D10
Keywords: Legendrian, Floer, Positive isotopies
@article{AIF_2019__69_4_1679_0,
     author = {Chantraine, Baptiste and Colin, Vincent and Dimitroglou Rizell, Georgios},
     title = {Positive Legendrian isotopies and Floer theory},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {69},
     number = {4},
     year = {2019},
     pages = {1679-1737},
     doi = {10.5802/aif.3279},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2019__69_4_1679_0}
}
Positive Legendrian isotopies and Floer theory. Annales de l'Institut Fourier, Volume 69 (2019) no. 4, pp. 1679-1737. doi : 10.5802/aif.3279. https://aif.centre-mersenne.org/item/AIF_2019__69_4_1679_0/

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