Generation of immersed Lagrangians by cocores

TL;DR

This paper extends a generation theorem to exact Lagrangian immersions in Weinstein manifolds, showing they are generated by cocores if equipped with an augmentation or bounding cochain.

Contribution

It generalizes the generation theorem to a broader class of Lagrangian immersions in Weinstein manifolds with new algebraic conditions.

Findings

Exact Lagrangian immersions with augmentations are generated by cocores.

The theorem applies to Weinstein manifolds with new algebraic criteria.

Provides a framework connecting augmentations and Lagrangian generation.

Abstract

We extend the generation theorem of Chantraine--Dimitroglou Rizell--Ghiggini--Golovko to exact Lagrangian immersions in Weinstein manifolds. We prove that an exact Lagrangian immersion equipped with an augmentation of the Chekanov--Eliashberg algebra of its Legendrian lift, or equivalently, equipped with a corresponding bounding cochain, is generated by the Lagrangian cocores.