Infinitely many monotone Lagrangian tori in $\mathbb{R}^6$

TL;DR

This paper constructs infinitely many distinct monotone Lagrangian tori in six-dimensional Euclidean space, distinguished by their bounded pseudo-holomorphic discs, demonstrating a rich diversity of such structures.

Contribution

It introduces infinitely many non-Hamiltonian isotopic monotone Lagrangian tori in , distinguished by their Maslov index 2 disc counts.

Findings

Infinitely many monotone Lagrangian tori in  constructed.

Tori are distinguished by arbitrarily large disc counts.

No two tori are related by Hamiltonian isotopy.

Abstract

We construct infinitely many families of monotone Lagrangian tori in $\mathbb{R}^6$, no two of which are related by Hamiltonian isotopies (or symplectomorphisms). These families are distinguished by the (arbitrarily large) numbers of families of Maslov index 2 pseudo-holomorphic discs that they bound.