On degree of smooth maps between orbifolds

Abstract

In the present work we develop the degree theory for proper maps between orbifolds of same dimension. The definition of degree for the mentioned maps was introduced by Pasquoto and Rot (2020). We propose a new, simpler definition for the degree of proper maps between smooth oriented orbifolds of the same dimension and show that it is equivalent to the definition by Pasquotto and Rot. Using this new approach, we establish a connection between the degree of a map and the integration of exterior forms on orbifolds, which is important for physical applications. We obtain an integral formula for the degree of a map between orbifolds, which is a generalization of the corresponding formula for manifolds. We also reveal the specificity of degree of a map for compact orbifolds.