The diffeological de Rham cohomology of G/H equals the Lie algebra cohomology of g/h for dense subgroup H of Lie group G.
van Est, Dense imbeddings of Lie groups
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The de Rham cohomology of a Lie group modulo a dense subgroup
The diffeological de Rham cohomology of G/H equals the Lie algebra cohomology of g/h for dense subgroup H of Lie group G.