On a theorem of Henri Cartan concerning the equivaraint cohomology

Liviu I. Nicolaescu

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On a theorem of Henri Cartan concerning the equivaraint cohomology

Liviu I. Nicolaescu

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Abstract

Suppose G is a compact Lie group and N is a closed normal subgroup of G acting freely on a smooth manifold X. The Cartan theorem alluded to in the title postulates the existence of a natural isomorphism between the G-equivariant cohomology X and the G/N-equivariant cohomology of X/N. In this note we use J. Kalkman's explicit isomorphism between the Cartan and Weil models of equivariant cohomology to show that 1) Cartan's theorem is a simple consequence of Chern-Weil's transgression formula and 2) explicitly describe this isomorphism at the cochain level.

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Liviu I. Nicolaescu. 2000-05-07. On a theorem of Henri Cartan concerning the equivaraint cohomology. https://arxiv.org/abs/math/0005068

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