Exact Lagrangian caps and non-uniruled Lagrangian submanifolds

Abstract

We make the elementary observation that the Lagrangian submanifolds of ${\mathbb{C}}^n$, for each $n\ge 3$, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and moreover have infinite relative Gromov width. The construction of these submanifolds use exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a 1-jet space admits an exact Lagrangian cap then its Legendrian contact homology DGA is acyclic.

16 pages, 1 figure. Added Remark 1.11. Added Section 3.2. Corrected the definition of the linearised complex. Filled in a gap in the proof of Theorem 1.6

References in corpus (6)

• Loose Legendrian embeddings in high dimensional contact manifolds
• Legendrian Ambient Surgery and Legendrian Contact Homology
• A note on the front spinning construction
• Closed exact Lagrangians in the symplectization of contact manifolds
• Exact Lagrangian caps of Legendrian knots
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Cited by in corpus (8)

• Floer theory for Lagrangian cobordisms
• The augmentation category map induced by exact Lagrangian cobordisms
• Coisotropic Hofer-Zehnder capacities and non-squeezing for relative embeddings
• Coisotropic Ekeland-Hofer capacities
• Riemannian distance and symplectic embeddings in cotangent bundle
• Exact Lagrangian caps of Legendrian knots
• Nontriviality results for the characteristic algebra of a DGA
• On Lagrangian embeddings of closed non-orientable 3-manifolds