Orbifolds via Groupoids

Orbifolds are generalizations of manifolds that allow certain singularities. They were originally defined using charts and atlases, similar to manifolds, but working with these atlases is hard, particularly when dealing with maps between orbifolds. Orbifolds can alternatively be defined using groupoids, and this approach gives a way to define maps between orbifolds that works well with homotopy theory. In this talk we will define orbifolds and orbispaces, and give examples using the groupoid definition. Additionally how the orbigroupoid category can be used as a basis for developing results about orbispaces will be touched on.