On Exotic Lagrangian Tori in CP^2

TL;DR

This paper constructs a new type of monotone Lagrangian torus in complex projective plane CP^2, demonstrating it is distinct from known examples by analyzing its holomorphic disc families.

Contribution

It introduces an exotic monotone Lagrangian torus in CP^2 and proves it is not Hamiltonian isotopic to classical tori using mirror symmetry techniques.

Findings

Bounds 10 families of Maslov index 2 holomorphic discs

Shows the torus is not Hamiltonian isotopic to Clifford or Chekanov tori

Uses mirror symmetry-inspired methods

Abstract

We construct an exotic monotone Lagrangian torus in CP^2 using techniques motivated by mirror symmetry. We show that it bounds 10 families of Maslov index 2 holomorphic discs, and it follows that this exotic torus is not Hamiltonian isotopic to the known Clifford and Chekanov tori.