Geodesic
Koszul duality and equivariant cohomology
Documenta mathematica, Tome 11 (2006), pp. 243-259.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G$ be a topological group such that its homology $H(G)$ with coefficients in a principal ideal domain $R$ is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between $G$-spaces and spaces over $BG$ to the Koszul duality between modules up to homotopy over $H(G)$ and $H^*(BG)$. This gives in particular a Cartan-type model for the equivariant cohomology of a $G$-space with coefficients in $R$. As another corollary, we obtain a multiplicative quasi-isomorphism $C^*(BG)\to H^*(BG)$. A key step in the proof is to show that a differential Hopf algebra is formal in the category of $A_\infty$ algebras provided that it is free over $R$ and its homology an exterior algebra.
Classification : 16S37, 55N91, 16E45, 55N10 
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     author = {Franz, Matthias},
     title = {Koszul duality and equivariant cohomology},
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     pages = {243--259},
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     volume = {11},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2006__11__a8/}
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Franz, Matthias. Koszul duality and equivariant cohomology. Documenta mathematica, Tome 11 (2006), pp. 243-259. http://geodesic.mathdoc.fr/item/DOCMA_2006__11__a8/