On homological coherence of discrete groups
On homological coherence of discrete groups
复制标题
论离散群的同源一致性
DOI：
10.1016/j.jalgebra.2004.02.006
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发表时间：
2004
影响因子：
0.9
通讯作者：
B. Goldfarb
中科院分区：
文献类型：
--
作者：
G. Carlsson;B. Goldfarb
我们探讨了F. Waldhausen研究的离散群的相干性的弱化。这个新概念是根据群的粗几何定义的，对于计算它们的K-理论应该是有用的。证明了渐近维数有限的群Γ是弱凝聚的.特别地，当R是有限维正则环时，存在大量的有限同调维数的R[Γ]-模。这个类包含字双曲群，Coxeter群和，正如我们所展示的，连通李群的余紧离散子群。
We explore a weakening of the coherence property of discrete groups studied by F. Waldhausen. The new notion is defined in terms of the coarse geometry of groups and should be as useful for computing their K-theory. We prove that a group Γ of finite asymptotic dimension is weakly coherent. In particular, there is a large collection of R[Γ]-modules of finite homological dimension when R is a finite-dimensional regular ring. This class contains word-hyperbolic groups, Coxeter groups and, as we show, the cocompact discrete subgroups of connected Lie groups.