A transverse averaging operator built from infinitesimal data preserves basic cohomology classes and yields H^•_dR(G/H) ≅ H^•(g, h) when g is compact type and G/closure(H) is compact.
Reinhart,Harmonic integrals on foliated manifolds, Amer
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A Transverse Averaging Operator and Cohomology of Quotients by Non-closed Subgroups
A transverse averaging operator built from infinitesimal data preserves basic cohomology classes and yields H^•_dR(G/H) ≅ H^•(g, h) when g is compact type and G/closure(H) is compact.