A proof of Thurston's uniformization theorem of geometric orbifolds (Q808484)

A smooth m-dimensional orbifold is a \(\sigma\)-compact Hausdorff space M which is locally modelled on the quotient space of a finite group action on a smooth m-dimensional manifold. There is a corresponding notion of an orbifold covering, in which the local charts respect the covering map. A connected orbifold M is good if there exists an orbifold covering h: \(N\to M\) in which N is a manifold. A geometry (G,X) is a smooth connected manifold and a subgroup G of Diff(X). An orbifold modelled on (G,X) is called a (G,X)-orbifold. The paper proves the following theorem: Let (G,X) be a geometry such that if two diffeomorphisms belonging to G coincide on a non-empty subset of X then they coincide on X. Then every (G,X)-orbifold is good.