Lagrangian product tori in tame symplectic manifolds

TL;DR

This paper extends the classification of product Lagrangian tori from standard symplectic space to tame symplectically aspherical manifolds, highlighting the necessity of the asphericity condition through examples.

Contribution

It generalizes the classification of product Lagrangian tori to a broader class of symplectic manifolds, emphasizing the importance of the asphericity assumption.

Findings

Classification extended to tame symplectically aspherical manifolds

Examples show asphericity cannot be omitted

Highlights the role of asphericity in symplectic topology

Abstract

Product Lagrangian tori in standard symplectic space $R^{2n}$ were classified up to symplectomorphism in [Che96]. We extend this classification to tame symplectically aspherical symplectic manifolds. We show by examples that the asphericity assumption cannot be omitted.