The Differential Structure of an Orbifold

TL;DR

This paper demonstrates that the set of smooth functions on an orbifold uniquely determines its structure, establishing a functor from orbifolds to differential spaces.

Contribution

It proves that the underlying set and smooth functions of an orbifold fully determine its atlas, linking orbifolds to differential spaces.

Findings

The orbifold structure is uniquely determined by its smooth functions.

A functor from orbifolds to differential spaces is established.

The result bridges orbifold theory and differential space theory.

Abstract

We prove that the underlying set of an orbifold equipped with the ring of smooth real-valued functions completely determines the orbifold atlas. Consequently, we obtain an essentially injective functor from orbifolds to differential spaces.