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| Geometric Property （T） | |
| 作者姓名： | Rufus WILLETT Guoliang YU |
| 作者单位： | Department of Mathematics, University of Hawai’i at Mˉanoa.;Department of Mathematics, Texas A&M University, Shanghai Center for Mathematical Sciences. |
| 基金项目： | This work was supported by the U.S. National Science Foundation （Nos. DMS1229939, DMS1342083, DMS1362772）. |
| 摘 要： | This paper discusses“geometric property （T）”. This is a property of metric spaces introduced in earlier works of the authors for its applications to K-theory. Geometric property （T） is a strong form of “expansion property”, in particular, for a sequence （Xn） of bounded degree finite graphs, it is strictly stronger than （Xn） being an expander in the sense that the Cheeger constants h（Xn） are bounded below. In this paper, the authors show that geometric property （T） is a coarse invariant, i.e., it depends only on the large-scale geometry of a metric space X. The authors also discuss how geometric property （T） interacts with amenability, property （T） for groups, and coarse geometric notions of a-T-menability. In particular, it is shown that property （T） for a residually finite group is characterised by geometric property （T） for its finite quotients. |
| 关 键 词： | 几何性质 几何属性 度量空间 膨胀特性 剩余有限群 K-理论 几何概念 显示属性 |
| 收稿时间： | 2026/11/13 0:00:00 |
Geometric Property (T) |
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| Rufus WILLETT,Guoliang YU.Geometric Property (T)[J].Chinese Annals of Mathematics,Series B,2014,35(5):761-800. | |
| Authors: | Rufus WILLETT and Guoliang YU |
| Institution: | 1. Department of Mathematics, University of Hawai’i at Mānoa, Honolulu, USA 2. Department of Mathematics, Texas A&M University, College Station, USA 3. Shanghai Center for Mathematical Sciences, Shanghai, China |
| Abstract: | This paper discusses “geometric property (T)”. This is a property of metric spaces introduced in earlier works of the authors for its applications to K-theory. Geometric property (T) is a strong form of “expansion property”, in particular, for a sequence (X n ) of bounded degree finite graphs, it is strictly stronger than (X n ) being an expander in the sense that the Cheeger constants h(X n ) are bounded below. In this paper, the authors show that geometric property (T) is a coarse invariant, i.e., it depends only on the large-scale geometry of a metric space X. The authors also discuss how geometric property (T) interacts with amenability, property (T) for groups, and coarse geometric notions of a-T-menability. In particular, it is shown that property (T) for a residually finite group is characterised by geometric property (T) for its finite quotients. |
| Keywords: | Coarse geometry Expander Roe algebra Property (T) |
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