Roe $$C^*$$C∗-algebra for groupoids and generalized Lichnerowicz vanishing theorem for foliated manifolds
Roe $$C^*$$C∗-algebra for groupoids and generalized Lichnerowicz vanishing theorem for foliated manifolds
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DOI：
10.1007/s00209-018-2064-7
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发表时间：
2016-05
影响因子：
0.8
通讯作者：
Xiang Tang;R. Willett;Yi-jun Yao
中科院分区：
文献类型：
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作者：
Xiang Tang;R. Willett;Yi-jun Yao
本文对单位空间一般不紧的局部紧广群引入Roe-代数的概念，并使其具有适当的粗结构和Haar系。利用Connes的切群胚方法，在具有额外度量结构的李群胚上引入椭圆微分算子的解析指标，该指标取Roe-代数的K-理论中的值.我们应用我们的理论导出了开流形上的叶理的一个Lichnerowicz型消失结果。
We introduce the concept of Roe-algebra for a locally compact groupoid whose unit space is in general not compact, and that is equipped with an appropriate coarse structure and Haar system. Using Connes’ tangent groupoid method, we introduce an analytic index for an elliptic differential operator on a Lie groupoid equipped with additional metric structure, which takes values in the K-theory of the Roe-algebra. We apply our theory to derive a Lichnerowicz type vanishing result for foliations on open manifolds.