A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}

Details A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1} A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}

2011-08-18

arxiv.org/abs/1108.3693v4

Mathematics

Symplectic Geometry

14 pages, 2 figures; some typos and inessential mistakes have been corrected, the statement of Theorem 1.4 has been modified

Scientific paper

We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R^{2n+1}. More precisely, we investigate the behavior of the Thurston-Bennequin number and (linearized) Legendrian contact homology under this relation. The result about the Thurston-Bennequin number can be considered as a generalization of the result of Chantraine which holds when n=1. In addition, we provide a few constructions of Lagrangian cobordisms and prove that there are infinitely many pairs of Lagrangian cobordant and not Legendrian isotopic Legendrian n-tori in R^{2n+1}.

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