Lie Algebras and the Four Color Theorem

TL;DR

This paper establishes a surprising equivalence between a statement in Lie algebra theory and the Four Color Theorem, linking algebraic structures to a famous graph coloring problem.

Contribution

It introduces a novel algebraic formulation equivalent to the Four Color Theorem, connecting Lie algebras with knot invariants and 3-manifold theory.

Findings

Lie algebra statement equivalent to Four Color Theorem

Connections to Vassiliev invariants and 3-manifolds

Bridges algebraic and topological graph coloring concepts

Abstract

We present a ``reasonable'' statement about Lie algebras that is equivalent to the Four Color Theorem. The notions appearing in the statement also appear in the theory of finite-type invariants of knots (Vassiliev invariants) and 3-manifolds.