代数K理论中的连续控制分裂
Splitting With Continuous Control in Algebraic K-theory
摘要：
在这项工作中，连续控制装配映射的代数$K$理论，由Carlsson和Pedersen，被证明是一个分裂注入组$Γ$，满足一定的几何条件。允许群$Γ$有挠，推广了Carlsson和Pedersen的一个结果.结合John Moody的一个结果，当$Γ$是虚循环群且$k$是特征零域时，证明了$K_0(kΓ)$同构于$K_0(kH)$在$Γ$的有限子群$H$上的余极限.
英文摘要：
In this work, the continuously controlled assembly map in algebraic $K$-theory, as developed by Carlsson and Pedersen, is proved to be a split injection for groups $Γ$ that satisfy certain geometric conditions. The group $Γ$ is allowed to have torsion, generalizing a result of Carlsson and Pedersen. Combining this with a result of John Moody, $K_0(kΓ)$ is proved to be isomorphic to the colimit of $K_0(kH)$ over the finite subgroups $H$ of $Γ$, when $Γ$ is a virtually polycyclic group and $k$ is a field of characteristic zero.
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