Algebraic K-theory over virtually abelian groups☆
Algebraic K-theory over virtually abelian groups☆
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几乎阿贝尔群上的代数 K 理论☆
DOI：
10.1016/j.jpaa.2011.06.001
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发表时间：
2012
影响因子：
0.8
通讯作者：
F. Quinn
中科院分区：
文献类型：
--
作者：
F. Quinn
利用受控K-理论证明了映射到虚拟阿贝尔群的群的代数K-理论是由目标群的超基本子群(可能是无限的)定义的集合图来描述的。这些子群是虚拟循环的，因此结果是对(纤化的)Farrell-Jones猜想的改进，即K-理论来自虚拟循环群。一个推论是，对于任何一个群体，法雷尔-琼斯猜想都等同于这个精炼版本。
Controlled K-theory is used to show that algebraic K-theory of a group mapping to a virtually abelian group is described by an assembly map defined using hyperelementary subgroups (possibly infinite) of the target group. These subgroups are virtually cyclic, so the result is a refinement of the (fibered) Farrell–Jones conjecture that K-theory comes from virtually cyclic groups. A corollary is that for any group, the Farrell–Jones conjecture is equivalent to this refined version.