论文标题
非污点空间的几何特性（T）
Geometric property (T) for non-discrete spaces
论文作者
论文摘要
几何特性（T）由Willett和Yu定义，首先是图形序列，然后是更通用的离散空间。具有几何特性（T）的图形序列增加是扩展器，它们是粗大空间的示例，最大粗糙的Baum-connes组装图无法过多地溢出。在这里，我们给出了包含非差异空间的粗空间的有界几何形状的更广泛的定义。我们为这类空间定义了几何特性（T）的概括，并表明它是一个粗糙的不变性。此外，我们以拉普拉斯主义者的光谱特性来表征它。我们研究了流形和扭曲系统的几何特性（T）。
Geometric property (T) was defined by Willett and Yu, first for sequences of graphs and later for more general discrete spaces. Increasing sequences of graphs with geometric property (T) are expanders, and they are examples of coarse spaces for which the maximal coarse Baum-Connes assembly map fails to be surjective. Here, we give a broader definition of bounded geometry for coarse spaces, which includes non-discrete spaces. We define a generalisation of geometric property (T) for this class of spaces and show that it is a coarse invariant. Additionally, we characterise it in terms of spectral properties of Laplacians. We investigate geometric property (T) for manifolds and warped systems.
