Exact Lagrangian tori in $T^*\mathbb{T}^n$

TL;DR

The paper constructs an exact Lagrangian submanifold in the cotangent bundle of an n-torus that is symplectically but not Hamiltonian isotopic to the zero section, revealing new distinctions in symplectic topology.

Contribution

It demonstrates the existence of such Lagrangian submanifolds in higher dimensions, expanding understanding of symplectic and Hamiltonian isotopy classes.

Findings

Existence of exact Lagrangian in $T^* ext{T}^n$ not Hamiltonian isotopic to zero section

Distinction between symplectic and Hamiltonian isotopy classes in higher dimensions

New examples in symplectic topology showing richer structure

Abstract

We show that for $n\geq 2$ there exists an exact Lagrangian submanifold $L$ in the cotangent bundle $T^*\mathbb{T}^n$ of the $n$-dimensional torus $\mathbb{T}^n$ such that $L$ is symplectically but not Hamiltonian isotopic to the zero section of $T^*\mathbb{T}^n$.