Relatively hyperbolic groups, rapid decay algebras and a generalization of the Bass conjecture
Relatively hyperbolic groups, rapid decay algebras and a generalization of the Bass conjecture
复制标题
相对双曲群、快速衰减代数和巴斯猜想的推广
DOI：
10.4171/jncg/50
复制
发表时间：
2007
影响因子：
0.9
通讯作者：
B. Ramsey
中科院分区：
文献类型：
--
作者：
R. Ji;C. Ogle;B. Ramsey
利用Connes的循环同调理论，通过构造1.G/的稠密子代数，推广了Bass猜想.特别是，我们提出了一个更强的版本的` 1 -Bass猜想。证明了双曲群相对于每个子群都具有多项式共轭界性质和幂零周期性质的1000个子群满足1 -Stronger-Bass猜想.此外，我们确定了相对双曲群的共轭界，并计算了任意双曲群的1 -代数的循环上同调
By deploying dense subalgebras of ` 1 .G/ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the ` 1 -Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy bound property and nilpotent periodicity property, satisfy the ` 1 -Stronger-Bass Conjecture. Moreover, we determine the conjugacy bound for relatively hyperbolic groups and compute the cyclic cohomology of the ` 1 -algebra of any