论文标题
ROE代数的变体，用于具有圆柱形末端的空间，并在相对较高指数理论中应用
A Variant of Roe Algebras for Spaces with Cylindrical Ends with Applications in Relative Higher Index Theory
论文作者
论文摘要
在本文中，我们为具有圆柱形末端的空间定义了ROE代数的变体，并使用此问题来研究有关在圆柱端上串制的歧管上的正标曲率指标的存在和分类的问题。我们讨论了我们的构造如何与Chang，Weinberger和Yu开发的相对较高索引理论相关，并利用这种关系来定义具有边界歧管上的正标度曲率指标的较高的Rho不变。这为分类这些指标铺平了道路。最后，我们使用此处开发的机械来提供Schick和作者结果的简洁证明，该证明将相对较高的索引与在边界上存在正标曲率存在下定义的索引相关联。
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.
