Existence of Orbifolds IV: Examples

Abstract

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete topological base spaces associated to such orbifolds can be described and manipulated in our universal language. At the same time, we interpret our many categorical axioms in several explicit contexts.