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The Grauert--Grothendieck complex on differentiable spaces and a sheaf complex of Brylinski
Markus J. Pflaum, Hessel B. Posthuma and Xiang Tang
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.