相对几何装配与映射锥，第一部分：几何模型及其应用
Relative geometric assembly and mapping cones, Part I: The geometric model and applications
摘要：
受Chang，Weinberger和Yu的一个解析构造的启发，我们定义了相对几何$K$ -同调中的装配映射.使用各种索引理论工具（例如，局域化指数和更高的Atiyah-Patodi-Singer指数理论）。作为应用，我们得到了具有边界和正数量曲率的流形的一个消失结果，这个结果也受到了Chang，Weinberger和Yu的启发.进一步，我们利用Wahl的结果证明了相对集合映射的有理内射性蕴涵了带边界带边流形的相对高阶特征标的同伦不变性.
英文摘要：
Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric $K$-homology. The properties of the geometric assembly map are studied using a variety of index theoretic tools (e.g., the localized index and higher Atiyah-Patodi-Singer index theory). As an application we obtain a vanishing result in the context of manifolds with boundary and positive scalar curvature; this result is also inspired and connected to work of Chang, Weinberger and Yu. Furthermore, we use results of Wahl to show that rational injectivity of the relative assembly map implies homotopy invariance of the relative higher signatures of a manifold with boundary.
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