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We use the Grauert--Grothendieck complex on differentiable spaces to studybasic relative forms on the inertia space of a compact Lie group action on amanifold. We prove that the sheaf complex of basic relative forms on theinertia space is a fine resolution of Bryliski's sheaf of functions on theinertia space.

The Grauert--Grothendieck complex on differentiable spaces and a sheaf complex of Brylinski