论文标题
参数化K理论中的渐近转移图
Asymptotic transfer maps in parametrized K-theory
论文作者
论文摘要
我们在有限的K理论中定义了渐近转移，以及可以在一般性方面完成的上下文。受控代数在几何拓扑中的许多进步中都起着核心作用，包括在Novikov，Borel和Farrell-Jones的最新工作。从Farrell和Jones的原始作品开始，在整个主题中出现的各种表现形式中出现的特征之一是渐近转移，其含义和构造取决于几何环境。我们首先开发了一个通用框架，使我们能够为任何有限的非球形综合体构建一个渐近转移图的版本。该框架是具有纤维控制的模棱两可的参数化K理论。我们还包括几个用于计算的纤维切除定理以及对标准工具分解的位置以及哪些工具取代它们的讨论。
We define asymptotic transfers in bounded K-theory together with a context where this can be done in great generality. Controlled algebra plays a central role in many advances in geometric topology, including recent work on Novikov, Borel, and Farrell-Jones conjectures. One of the features that appears in various manifestations throughout the subject, starting with the original work of Farrell and Jones, is an asymptotic transfer whose meaning and construction depend on the geometric circumstances. We first develop a general framework that allows us to construct a version of asymptotic transfer maps for any finite aspherical complex. This framework is the equivariant parametrized K-theory with fibred control. We also include several fibrewise excision theorems for its computation and a discussion of where the standard tools break down and which tools replace them.
