Geodesic
Koszul duality and equivariant cohomology
Documenta mathematica, Tome 11 (2006), pp. 243-259
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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)→H∗(BG). A key step in the proof is to show that a differential Hopf algebra is formal in the category of A∞​ algebras provided that it is free over R and its homology an exterior algebra.
DOI : 10.4171/dm/211
Classification : 16E45, 16S37, 55N10, 55N91 
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     author = {Matthias Franz},
     title = {Koszul duality and equivariant cohomology},
     journal = {Documenta mathematica},
     pages = {243--259},
     year = {2006},
     volume = {11},
     doi = {10.4171/dm/211},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/211/}
}
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Matthias Franz. Koszul duality and equivariant cohomology. Documenta mathematica, Tome 11 (2006), pp. 243-259. doi: 10.4171/dm/211

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