Special case: quotient spaces \(M/G\) for \(G\) a compact Lie group acting smoothly on a smooth manifold. In this case \({ { {H}^{\scriptscriptstyle \bullet}} }(M/G) \cong { { {H}^{\scriptscriptstyle \bullet}} }_G(M)\), where the first is orbifold cohomology and the second is \(G{\hbox{-}}\)equivariant homology.