Abstract
This chapter looks at the Cartan model. Specifically, it generalizes the Cartan model from a circle action to a connected Lie group action. The chapter assumes the Lie group to be connected, because the condition that LX α = 0 is sufficient for a differential form α on M to be invariant holds only for a connected Lie group. It also considers the theorem that marks the transition from the Weil model to the Cartan model. It is due to Henri Cartan, who played a crucial role in the development of equivariant cohomology. The chapter then studies the Weil-Cartan isomorphism.
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