On triangulations of orbifolds and formality (Q2084901)

Orbifolds are generalizations of manifolds, locally they are quotients of Euclidean spaces by smooth actions of finite groups. The underlying space of an orbifold can be stratified by the isotropy types, and it admits a triangulation as a stratified space. Orbifolds are naturally associated with two differential graded algebras. One of them is the DGA of orbifold differential forms, i.e., the orbifold de Rham algebra. If the underlying space of the orbifold admits a smooth triangulation, there is also the DGA of piecewise polynomial differential forms of the triangulation. The authors show that these two DGAs are weakly equivalent, which means that they are connected by a chain of quasi-isomorphisms. It follows that one of these DGAs is formal, if and only if the other one is. The authors also prove that global quotient orbifolds and global homogeneous isotropy orbifolds admit smooth triangulations.