Koszul duality and equivariant cohomology
| dc.creator | Franz, Matthias | |
| dc.date | 2003-07-09 | |
| dc.date | 2003-11-28 | |
| dc.date.accessioned | 2026-07-07T08:23:13Z | |
| dc.date.available | 2026-07-07T08:23:13Z | |
| dc.description | 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. 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-infinity algebras provided that it is free over R and its homology an exterior algebra. | |
| dc.description | 12 pages. v2: proof of Theorem 1.2 modified in Sec. 6, references added, other minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0307115 | |
| dc.identifier | http://arxiv.org/abs/math/0307115 | |
| dc.identifier | Documenta Math. 11 (2006), 243-259 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135919 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 16S37, 55N91 (primary), 16E45, 55N10 (secondary) | |
| dc.title | Koszul duality and equivariant cohomology | |
| dc.type | text |