Equivariant cohomology, Koszul duality, and the localization theorem

@article{Goresky1997EquivariantCK,
  title={Equivariant cohomology, Koszul duality, and the localization theorem},
  author={Mark Goresky and Robert E. Kottwitz and R. D. Macpherson},
  journal={Inventiones mathematicae},
  year={1997},
  volume={131},
  pages={25-83}
}
(1.1) This paper concerns three aspects of the action of a compact group K on a space X . The ®rst is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have the property that their cohomology may be computed from the structure of the zero and one dimensional orbits of the action of a maximal torus in K. (2) Koszul duality. This enables one to translate facts about equivariant cohomology into facts about its ordinary cohomology, and back. (3) Equivariant derived… 
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