A geometric proof of the Poincar\'e-Birkhoff-Witt Theorem

TL;DR

This paper presents a geometric proof of the Poincaré-Birkhoff-Witt Theorem leveraging the simply-connectedness of spheres for dimensions greater than or equal to two.

Contribution

It introduces a novel geometric approach to proving the Poincaré-Birkhoff-Witt Theorem, differing from traditional algebraic methods.

Findings

Geometric proof established for the PBW Theorem

Utilizes topological properties of spheres in the proof

Provides new insights into the theorem's foundational structure

Abstract

We use that the $n$-sphere for $n\geq 2$ is simply-connected to prove the Poincar\'e-Birkhoff-Witt Theorem.