Effective orbifolds were originally defined via charts and atlases, analogous to manifolds. In the current literature, they are often defined instead via certain topological groupoids, which gives a more convenient category for studying them. These two approaches are known to be equivalent and produce the same objects. More recently, applications arising in geometry and physics have led to an interest in more general ineffective orbifolds. However, the current generalizations of the atlas definition do not correspond to the objects created by ineffective topological groupoids. I will discuss a project, joint with D. Pronk and M. Tommasini, where we develop an alternate atlas definition for ineffective orbifolds. Our atlases generalize the existing effective atlas definition, and our definition leads to the same objects as those defined by ineffective topological groupoids.
Atlases for Ineffective Orbifolds Sponsored by the Meyer Fund
Atlases for Ineffective Orbifolds