A note on the cardinality of Lagrangian packings

TL;DR

This paper explores the possibility of packing uncountably many Lagrangian submanifolds within a symplectic manifold, considering both smooth and continuous categories.

Contribution

It investigates the cardinality constraints of Lagrangian packings in symplectic manifolds under different smoothness conditions.

Findings

Addresses $C^ abla$ and $C^0$ versions of the packing question

Analyzes the maximum possible number of Lagrangian submanifolds in a class

Provides insights into symplectic topology and Lagrangian embedding limitations

Abstract

Given a symplectic manifold, can one pack uncountably many Lagrangian submanifolds in a given Hamiltonian isotopy class of this symplectic manifold? We address $C^\infty$ and $C^0$ versions of this question.