# Degree theory for orbifolds

## TL;DR

This paper extends differential topology to orbifolds by defining a mapping degree for proper maps, demonstrating its invariance, and computing it in specific cases, thus advancing the mathematical understanding of orbifold mappings.

## Contribution

It introduces a new concept of mapping degree for orbifolds, including invariance properties and computational methods, building on previous foundational work.

## Key findings

- Mapping degree satisfies invariance properties under certain conditions.
- Degree can be computed explicitly in specific orbifold examples.
- The theory applies to proper maps without codimension one singularities.

## Abstract

In [3] Borzellino and Brunsden started to develop an elementary differential topology theory for orbifolds. In this paper we carry on their project by defining a mapping degree for proper maps between orbifolds, which counts preimages of regular values with appropriate weights. We show that the mapping degree satisfies the expected invariance properties, under the assumption that the domain does not have a codimension one singular stratum. We study properties of the mapping degree and compute the degree in some examples.