The equivariant de Rham complex on a simplicial G_*-manifold

Naoya Suzuki

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arXiv · 1605.01563

The equivariant de Rham complex on a simplicial G_*-manifold

Naoya Suzuki

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Abstract

We show that when a simplicial Lie group acts on a simplicial manifold $\{X_*\}$, we can construct a bisimplicial manifold and the de Rham complex on it. This complex is quasi-isomorphic to the equivariant simplicial de Rham complex on $\{X_*\}$ and its cohomology group is isomorphic to the cohomology group of the fat realization of the bisimplicial manifold. We also exhibit a cocycle in the equivariant simplicial de Rham complex.

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Naoya Suzuki. 2016-05-05. The equivariant de Rham complex on a simplicial G_*-manifold. https://arxiv.org/abs/1605.01563

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