关于Henri Cartan关于等价上同调的一个定理
On a theorem of Henri Cartan concerning the equivaraint cohomology
摘要：
设G是紧李群，N是G的自由作用在光滑流形X上的闭正规子群.在标题中提到的嘉当定理假设了G-等变上同调X和X/N的G/N-等变上同调之间存在自然同构。本文利用J. Kalkman关于等变上同调的Cartan模型和Weil模型之间的显式同构，证明了：1）Cartan定理是Chern-Weil超进公式的简单推论; 2）在上链水平上显式地描述了这种同构。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
