A note on Lagrangian cobordisms between Legendrian submanifolds of R²ⁿ⁺¹

الأصل · EN

We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R²ⁿ⁺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 exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian n-tori in R²ⁿ⁺¹.