子空间排列和性质T
Subspace Arrangements and Property T
摘要：
我们重新制定和推广的几何方法证明Kazhdan性质T的Dymara和Januszkiewicz开发和Ershov和Jaikin使用。主要结果是：由有限子群G_i生成的群G具有性质T，如果由每对子群生成的群具有性质T和足够大的Kazhdan常数。从本质上讲，Dymara和Januszkiewicz证明了相同的结果，但是我们对“足够大”的界限明显更好。作为这个结果的应用，我们给出了有限Coxeter群上随机游动关于标准生成集的Kazhdan常数和谱间隙的精确界，推广了Bacher和de la Hapre的一个结果.
英文摘要：
We reformulate and extend the geometric method for proving Kazhdan property T developed by Dymara and Januszkiewicz and used by Ershov and Jaikin. The main result says that a group G, generated by finite subgroups G_i, has property T if the group generated by each pair of subgroups has property T and sufficiently large Kazhdan constant. Essentially, the same result was proven by Dymara and Januszkiewicz, however our bound for "sufficiently large" is significantly better. As an application of this result, we give exact bounds for the Kazhdan constants and the spectral gaps of the random walks on any finite Coxeter group with respect to the standard generating set, which generalizes a result of Bacher and de la Hapre.
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