Axiomatic Differential Geometry II-3

TL;DR

This paper advances axiomatic differential geometry by establishing a general Jacobi identity, a fundamental result supporting the structure of vector fields within smooth geometry.

Contribution

It introduces a general Jacobi identity that underpins the Jacobi identity for vector fields in axiomatic differential geometry.

Findings

Established the general Jacobi identity in axiomatic differential geometry.

Linked the general Jacobi identity to the classical Jacobi identity for vector fields.

Contributed to the foundational understanding of smooth structures in differential geometry.

Abstract

As the fourth paper of our series of papers concerned with axiomatic differential geometry, this paper is devoted to the general Jacobi identity supporting the Jacobi identity of vector fields. The general Jacobi identity can be regarded as one of the few fundamental results belonging properly to smootheology.