Origin of emergent algebras

TL;DR

This paper explores the conceptual foundations of emergent algebras, particularly addressing why tangent spaces in sub-Riemannian geometry can be viewed as groups, offering insights into their algebraic structure.

Contribution

It provides an expository analysis of the tangent space as a group within the framework of emergent algebras, clarifying the algebraic underpinnings in sub-Riemannian geometry.

Findings

Tangent spaces in sub-Riemannian geometry can be understood as emergent algebraic structures.

Emergent algebras offer a framework to interpret tangent spaces as groups.

The article clarifies the algebraic reasons behind the group structure of tangent spaces.

Abstract

This is an expository article concerning the last section "Why is the tangent space a group?" (section 8) of the article by A. Bellaiche, The tangent space in sub-riemannian geometry, from the viewpoint of emergent algebras.