The Grauert--Grothendieck complex on differentiable spaces and a sheaf   complex of Brylinski
  We use the Grauert--Grothendieck complex on differentiable spaces to study basic relative forms on the inertia space of a compact Lie group action on a manifold. We prove that the sheaf complex of basic relative forms on the inertia space is a fine resolution of Bryliski's sheaf of functions on the inertia space. 
Markus J. Pflaum, Hessel B. Posthuma, and Xiang Tang
math.GT