Exact Lagrangian caps and non-uniruled Lagrangian submanifolds

TL;DR

The paper demonstrates that certain Lagrangian submanifolds in complex Euclidean spaces are non-uniruled with infinite Gromov width, and shows that Legendrian submanifolds with exact caps have acyclic contact homology.

Contribution

It establishes the non-uniruled nature and infinite Gromov width of specific Lagrangian submanifolds constructed via exact caps, and links exact caps to the acyclicity of Legendrian contact homology.

Findings

Constructed Lagrangian submanifolds are non-uniruled.

These submanifolds have infinite relative Gromov width.

Legendrian submanifolds with exact caps have acyclic contact homology.

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.