Infinitely many monotone Lagrangian tori in higher projective spaces

TL;DR

This paper extends the construction of infinitely many exotic monotone Lagrangian tori from the complex projective plane to higher-dimensional projective spaces, demonstrating their non-symplectomorphic nature.

Contribution

It generalizes Vianna's construction to higher dimensions and proves these tori are distinct using an elementary approach with wall-crossing formulas.

Findings

Existence of infinitely many non-symplectomorphic monotone Lagrangian tori in higher projective spaces.

Extension of Vianna's construction from the complex projective plane to higher dimensions.

Application of wall-crossing formulas to distinguish the tori.

Abstract

Vianna constructed infinitely many exotic Lagrangian tori in the complex projective plane. We lift these tori to higher-dimensional projective spaces and show that they remain non-symplectomorphic. Our proof is elementary except for an application of the wall-crossing formula by Pascaleff-Tonkonog.