Koszul duality and equivariant cohomology
Matthias FranzFachbereich Mathematik Universität Konstanz 78457 Konstanz Germany
Let be a topological group such that its homology with coefficients in a principal ideal domain is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between -spaces and spaces over to the Koszul duality between modules up to homotopy over and . This gives in particular a Cartan-type model for the equivariant cohomology of a -space with coefficients in . As another corollary, we obtain a multiplicative quasi-isomorphism . A key step in the proof is to show that a differential Hopf algebra is formal in the category of algebras provided that it is free over and its homology an exterior algebra.
Cite this article
Matthias Franz, Koszul duality and equivariant cohomology. Doc. Math. 11 (2006), pp. 243–259DOI 10.4171/DM/211