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

Markus J. Pflaum, Hessel B. Posthuma, and Xiang Tang

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Submission date: 19. May. 2016
Pages: 12
published in: Methods and applications of analysis, 24 (2017) 2, p. 321-332 
DOI number (of the published article): 10.4310/MAA.2017.v24.n2.a8
Bibtex
Keywords and phrases: G-manifold, Grauert-Grothendieck complex, Brylinski's sheaf
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Abstract:
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.