论文标题
在第一个$ \ ell^2 $ -betti编号的上限
On upper bounds for the first $\ell^2$-Betti number
论文作者
论文摘要
本文介绍了一种仅使用Cayley图的几何形状来证明第一个$ \ ell^2 $ betti组的上限的方法。作为一个应用程序，我们证明，大型指数的伯恩赛德小组已经消失了第一个$ \ ell^2 $ -betti号码。 我们的方法扩展到使用字符定义的$ \ ell^2 $ -betti编号的概括。我们通过将Thom-Peterson在Q-正常子组上概括为此设置来说明这种灵活性。
This article presents a method for proving upper bounds for the first $\ell^2$-Betti number of groups using only the geometry of the Cayley graph. As an application we prove that Burnside groups of large prime exponent have vanishing first $\ell^2$-Betti number. Our approach extends to generalizations of $\ell^2$-Betti numbers, that are defined using characters. We illustrate this flexibility by generalizing results of Thom-Peterson on q-normal subgroups to this setting.
