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

TL;DR

This paper explores how Lagrangian cobordisms relate to Legendrian submanifolds in high-dimensional contact spaces, analyzing invariants like Thurston-Bennequin number and Legendrian contact homology, and constructing examples of non-isotopic cobordant Legendrian tori.

Contribution

It generalizes known results about Thurston-Bennequin number to higher dimensions and provides new constructions of Lagrangian cobordisms between Legendrian submanifolds.

Findings

Thurston-Bennequin number behavior under Lagrangian cobordisms is characterized.

Existence of infinitely many non-isotopic Legendrian tori with Lagrangian cobordisms.

New constructions of Lagrangian cobordisms in high dimensions.

Abstract

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 exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian n-tori in R^{2n+1}.