Geodesic
Legendrian knots and exact Lagrangian cobordisms
Journal of the European Mathematical Society, Tome 18 (2016) no. 11, pp. 2627-2689

Voir la notice de l'article provenant de la source EMS Press

We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair (X,L) consisting of an exact symplectic manifold X and an exact Lagrangian cobordism L⊂X which agrees with cylinders over Legendrian links Λ+​ and Λ−​ at the positive and negative ends induces a differential graded algebra (DGA) map from the Legendrian contact homology DGA of Λ+​ to that of Λ−​. We give a gradient flow tree description of the DGA maps for certain pairs (X,L), which in turn yields a purely combinatorial description of the cobordism map for elementary cobordisms, i.e., cobordisms that correspond to certain local modifications of Legendrian knots. As an application, we find exact Lagrangian surfaces that fill a fixed Legendrian link and are not isotopic through exact Lagrangian surfaces.
DOI : 10.4171/jems/650
Classification : 57-XX, 53-XX
Keywords: Contact structure, Legendrian knot, exact Lagrangian cobordism, contact homology 
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     author = {Tobias Ekholm and Ko Honda and Tam\'as K\'alm\'an},
     title = {Legendrian knots and exact {Lagrangian} cobordisms},
     journal = {Journal of the European Mathematical Society},
     pages = {2627--2689},
     publisher = {mathdoc},
     volume = {18},
     number = {11},
     year = {2016},
     doi = {10.4171/jems/650},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/650/}
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Tobias Ekholm; Ko Honda; Tamás Kálmán. Legendrian knots and exact Lagrangian cobordisms. Journal of the European Mathematical Society, Tome 18 (2016) no. 11, pp. 2627-2689. doi: 10.4171/jems/650

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