Equivariant cohomology and the Maurer-Cartan equation

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dc.creatorAlekseev, A.
dc.creatorMeinrenken, E.
dc.date2004-06-17
dc.date2005-02-16
dc.date.accessioned2026-07-07T08:20:19Z
dc.date.available2026-07-07T08:20:19Z
dc.descriptionLet G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant differential forms. In this paper, we construct an explicit cochain map from the small Cartan model into the standard Cartan model, inducing an isomorphism in cohomology. The construction involves the solution of a remarkable inhomogeneous Maurer-Cartan equation. This solution has further applications to the theory of transgression in the Weil algebra, and to the Chevalley-Koszul theory of the cohomology of principal bundles.
dc.description33 pages. Final version, to appear in Duke Mathematical Journal
dc.identifierhttps://arxiv.org/abs/math/0406350
dc.identifierhttp://arxiv.org/abs/math/0406350
dc.identifierDuke Mathematical Journal 130 (2005), 479-521
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135038
dc.subjectDifferential Geometry
dc.subjectAlgebraic Topology
dc.titleEquivariant cohomology and the Maurer-Cartan equation
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