Relative hyperbolicity, classifying spaces, and lower algebraic K-theory
Relative hyperbolicity, classifying spaces, and lower algebraic K-theory
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相对双曲性、分类空间和低代数 K 理论
DOI：
10.1016/j.top.2007.03.001
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
I. J. Ortiz
中科院分区：
文献类型：
--
作者：
J.;I. J. Ortiz
对于Γ一个相对双曲群，我们在Γ的虚循环子群的VC族上构造了Γ-spaces间具有各向同性的泛空间模型。给出了O+(n,1)=Isom（Hn）中Coxeter群的极大无限虚循环子群的判别方法。我们使用我们获得的信息来显式计算Coxeter群Γ3（O+(3,1)中的非均匀晶格）的下代数k理论。部分计算涉及计算Z[D2]， Z[D3]的某些Waldhausen nil群。
For Γ a relatively hyperbolic group, we construct a model for the universal space among Γ-spaces with isotropy on the family VC of virtually cyclic subgroups of Γ. We provide a recipe for identifying the maximal infinite virtually cyclic subgroups of Coxeter groups which are lattices in O+(n,1)=Isom(Hn). We use the information we obtain to explicitly compute the lower algebraic K-theory of the Coxeter group Γ3(a non-uniform lattice in O+(3,1)). Part of this computation involves calculating certain Waldhausen Nil-groups for Z[D2], Z[D3].