# Integration of 1-forms and connections

## TL;DR

This paper provides a combinatorial and geometric proof that a torsion-free and curvature-free affine connection implies the local structure of an affine space.

## Contribution

It offers a novel combinatorial and geometric argument for a classical differential geometry result about affine connections.

## Key findings

- Affine connection with zero torsion and curvature is locally an affine space.
- Provides a new proof technique combining combinatorial and geometric methods.
- Clarifies the local structure of special affine connections.

## Abstract

We give a combinatorial/geometric argument of the classical result that an affine connection, which is both torsion free and curvature free, is locally an affine space.