A homology theory for étale groupoids
A homology theory for étale groupoids
复制标题
étale群胚的同源理论
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
I. Moerdijk
中科院分区：
文献类型：
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作者：
M. Crainic;I. Moerdijk
Etale群形自然地作为轨道折叠叶空间和离散群作用轨道空间的模型而出现。在本文中，我们介绍了etale群形的层同调理论。我们证明了它在Morita等价下的不变性以及Haeiger上同调和该同调之间的Verdier对偶性我们还讨论了与Connes卷积代数的循环和Hochschild同调的关系 群群并导出一些谱序列，作为计算这些同源性的工具
Etale groupoids arise naturally as models for leaf spaces of foliations for orbifolds and for orbit spaces of discrete group actions In this paper we introduce a sheaf homology theory for etale groupoids We prove its invariance under Morita equivalence as well as Verdier duality between Haeiger cohomology and this homology We also discuss the relation to the cyclic and Hochschild homologies of Connes convolution algebra of the groupoid and derive some spectral sequences which serve as a tool for the computation of these homologies