A Note on Lagrangian Submanifolds in Symplectic $4m$-Manifolds

TL;DR

This paper identifies a topological obstruction that prevents certain Lagrangian submanifolds from existing in symplectic manifolds of dimension 4m, contributing to the understanding of symplectic topology.

Contribution

It introduces a new topological obstruction criterion for the existence of specific Lagrangian submanifolds in symplectic 4m-manifolds.

Findings

Identifies a topological obstruction to Lagrangian submanifolds

Provides conditions under which certain Lagrangians cannot exist

Enhances understanding of symplectic topology constraints

Abstract

This short paper shows a topological obstruction of the existence of certain Lagrangian submanifolds in symplectic $4m$-manifolds.