柱端空间Roe代数的一个变形及其在相对高指标理论中的应用
A Variant of Roe Algebras for Spaces with Cylindrical Ends with Applications in Relative Higher Index Theory
摘要：
在本文中，我们定义了一个变种的Roe代数的空间与圆柱形的结束，并使用此研究问题的存在性和分类的度量的正数量曲率的流形上的collared在圆柱形的结束。我们讨论了我们的建设是如何相关的相对较高的指标理论开发的张，温伯格，俞和使用这种关系来定义更高的ρ-不变量的正数量曲率度量流形上的边界。这为这些指标的分类铺平了道路。最后，我们使用这里开发的机器给出了一个简洁的证明结果的Schick和作者，其中涉及的相对较高的指数定义在存在的正数量曲率的边界上的指数。
英文摘要：
In this paper we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. This paves the way for classification of these metrics. Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.
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