We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the equivariant cohomology of a differentiable stack generalising among others Bott's spectral sequence which converges to the cohomology of the classifying space of a Lie group.

中文翻译：

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可微栈的等变上同调

我们构建并分析了可微堆栈的等变上同调模型，李群作用扩展了由于 Borel、Cartan 和 Getzler 导致的光滑流形的经典结果。我们还导出了可微堆栈的等变上同调的各种谱序列，其中概括了 Bott 谱序列，该谱序列收敛到李群的分类空间的上同调。