01 December 05 Equivariant cohomology and the Maurer-Cartan equation
A. Alekseev, E. Meinrenken
Author Affiliations +
Duke Math. J. 130(3): 479-522 (01 December 05). DOI: 10.1215/S0012-7094-05-13033-2

Abstract

Let G be a compact, connected Lie group acting smoothly on a manifold M. In their 1998 article [7], Goresky, Kottwitz, and MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard (large) Cartan complex of equivariant differential forms. In this article, we construct an explicit cochain map from the small Cartan model into the large Cartan model, intertwining the (Sg*)inv-module structures and 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

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A. Alekseev. E. Meinrenken. "Equivariant cohomology and the Maurer-Cartan equation." Duke Math. J. 130 (3) 479 - 522, 01 December 05. https://doi.org/10.1215/S0012-7094-05-13033-2

Information

Published: 01 December 05
First available in Project Euclid: 1 December 2005

zbMATH: 1085.57022
MathSciNet: MR2184568
Digital Object Identifier: 10.1215/S0012-7094-05-13033-2

Subjects:
Primary: 57R91
Secondary: 57T10

Rights: Copyright © 2005 Duke University Press

Vol.130 • No. 3 • 01 December 05
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