Koszul duality and equivariant cohomology

  • Matthias Franz

    Fachbereich Mathematik Universität Konstanz 78457 Konstanz Germany
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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.

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Matthias Franz, Koszul duality and equivariant cohomology. Doc. Math. 11 (2006), pp. 243–259

DOI 10.4171/DM/211