Low-area Floer theory and non-displaceability

TL;DR

This paper develops a new Floer theory focusing on least area holomorphic disks to establish non-displaceability of certain Lagrangian tori in complex surfaces, advancing symplectic topology methods.

Contribution

It introduces a novel Floer theory based on minimal area disks for non-monotone Lagrangians, enabling new non-displaceability results.

Findings

Proves non-displaceability of Lagrangian tori in complex projective plane.

Extends Floer theory to non-monotone settings using least area disks.

Establishes non-displaceability in del Pezzo surfaces.

Abstract

We introduce a new version of Floer theory of a non-monotone Lagrangian submanifold which only uses least area holomorphic disks with boundary on it. We use this theory to prove non-displaceability theorems about continuous families of Lagrangian tori in the complex projective plane and other del Pezzo surfaces.