Notes on monotone Lagrangian twist tori

TL;DR

This paper constructs and classifies monotone Lagrangian tori in various symplectic manifolds, demonstrating their non-displaceability and providing methods for their classification up to symplectomorphism and Hamiltonian isotopy.

Contribution

It introduces new constructions of monotone Lagrangian tori in multiple symplectic spaces and offers a classification framework distinguishing them up to symplectomorphism and isotopy.

Findings

Constructed monotone Lagrangian tori in standard symplectic vector space, projective space, and products of spheres.

Provided classification methods for these tori up to symplectomorphism and Hamiltonian isotopy.

Proved that these tori are non-displaceable by Hamiltonian isotopies.

Abstract

We construct monotone Lagrangian tori in the standard symplectic vector space, in the complex projective space and in products of spheres. We explain how to classify these Lagrangian tori up to symplectomorphism and Hamiltonian isotopy, and how to show that they are not displaceable by Hamiltonian isotopies.