A note on Lagrangian cobordisms between Legendrian submanifolds of \(\mathbb R^{2n+1}\) (Q1951185)

This paper is devoted to the study of embedded Lagrangian cobordisms between closed orientable Legendrian submanifolds of \(\mathbb R ^{ 2n+1}\). Exact Lagrangian cobordism between two Legendrian submanifolds can be used to define a map between the Legendrian contact homology algebras. The main result of this paper is related to the study of the behavior of the Thurston-Bennequin number and linearized Legendrian contact homology. In particular a generalization of Chantraine's result for \(n=1\) is obtained. Also, examples of Lagrangian cobordisms are described, in particular exact Lagrangian cobordisms between non-isotopic Legendrian \(n\)-tori in \(\mathbb R^{2n+1}\) are constructed and it is proved that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian \(n\)-tori in \(\mathbb R^{2n+1}\).