The coisotropic embedding theorem for pre-symplectic manifolds: an alternative proof

TL;DR

This paper offers an alternative algebraic proof of the Coisotropic Embedding Theorem for pre-symplectic manifolds, connecting geometric and algebraic perspectives through cotangent bundle embeddings.

Contribution

It introduces a novel proof method that recasts geometric choices as algebraic embeddings, providing new insights into the structure of pre-symplectic manifolds.

Findings

The proof links geometric connections to algebraic embeddings.

Identifies symplectic thickening via Hamiltonian momenta.

Provides a new perspective on coisotropic embeddings.

Abstract

We present an alternative proof of the Coisotropic Embedding Theorem in which the geometric choice of a connection is recast as the algebraic choice of an embedding into the cotangent bundle. The symplectic thickening is then identified as the submanifold determined by the Hamiltonian momenta conjugate to the kernel directions of the pre-symplectic form.