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

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}.

14 pages, 2 figures; improved exposition, many minor corrections, this version has been accepted for publication in the Pacific Journal of Mathematics

References in corpus (3)

• Legendrian Ambient Surgery and Legendrian Contact Homology
• Rational Symplectic Field Theory over Z_2 for exact Lagrangian cobordisms
• Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology

Cited by in corpus (11)

• Symplectic homology and the Eilenberg-Steenrod axioms
• Lagrangian Cobordisms via Generating Families: Constructions and Geography
• Floer theory for Lagrangian cobordisms
• Obstructions to Lagrangian concordance
• Obstructions to Lagrangian Cobordisms between Legendrians via Generating Families
• A note on the front spinning construction
• On homological rigidity and flexibility of exact Lagrangian endocobordisms
• Topologically Distinct Lagrangian and Symplectic Fillings
• Legendrian Satellites and Decomposable Concordances
• On non-geometric augmentations in high dimensions
• Lagrangian concordance is not a partial order in high dimensions