Monodromy and isotopy of monotone Lagrangian tori

TL;DR

This paper introduces new Hamiltonian isotopy invariants for monotone Lagrangian tori in symplectic 4-manifolds, demonstrating their effectiveness in distinguishing between different known tori in standard symplectic space.

Contribution

It defines novel invariants that differentiate monotone Lagrangian tori, specifically distinguishing the Clifford and Chekanov tori in symplectic 4-space.

Findings

Invariants distinguish Clifford and Chekanov tori

New invariants are effective in symplectic topology

Advances understanding of Lagrangian torus classification

Abstract

We define new Hamiltonian isotopy invariants for a monotone Lagrangian torus embedded in a symplectic 4-manifold. We show that, in the standard symplectic 4-space, these invariants distinguish a monotone Clifford torus from a Chekanov torus.