The de Rham complex on a bisimplicial manifold
Year: 2016
Type: preprint
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 show also how to construct a cocycle in the de Rham complex on a bisimplicial manifold $NG \rtimes NG$.
Source: arXiv (Cornell University)
Author: Naoya Suzuki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2345722428