Singular symplectic spaces and holomorphic membranes

TL;DR

This paper develops a topological framework for degenerating symplectic manifolds into singular spaces, focusing on Lagrangian manifolds and membranes, and reveals how such degenerations can produce exotic Lagrangian tori.

Contribution

It introduces a new topological approach to study degenerations of symplectic manifolds into singular spaces, emphasizing Lagrangian structures and membranes.

Findings

Degenerations into singular toric varieties yield exotic Lagrangian tori.

A topological framework for symplectic degenerations is established.

Holomorphic membranes are analyzed in the context of singular degenerations.

Abstract

We set up a topological framework for degenerations of symplectic manifolds into singular spaces paying a special attention to the behavior of Lagrangian manifolds and their (holomorphic) membranes. We show that degenerations into singular toric varieties provide a source of exotic Lagrangian tori.