Notes on word hyperbolic groups
Notes on word hyperbolic groups
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关于单词双曲群的注释
DOI：
10.1007/s00039-003-0425-8
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
H. Short
中科院分区：
文献类型：
--
作者：
J. Alonso;T. Brady;D. Cooper;V. Ferlini;Lustig;M. Mihalik;M. Shapiro;H. Short
设Γ是由有限集生成的群。给出了Γ具有Kazhdan性质(T)的一个充分条件。这个条件很容易检查，并且给出了Kazhdan常量。我们给出了这种方法适用的群的例子。我们证明了在某些情况下，一般表示定义了满足这一条件并因此具有性质(T)的群。此外，我们证明了满足这一条件的群的表示的微小变化不会改变群具有性质(T)的事实。
Let Γ be a group generated by a finite setS. We give a sufficient condition for Γ to have Kazhdan's property (T). This condition is easy to check and gives Kazhdan constants. We give examples of groups to which this method applies. We prove that in some setting generic presentations define groups which satisfy this condition and thus have property (T). Moreover we prove that small changes in the presentation of a group satisfying this condition do not change the fact that the group has property (T).