论文标题
带有Banach系数的Garland方法
Garland's method with Banach coefficients
论文作者
论文摘要
我们证明了Garland的Banach版本，该方法证明了对朴素复合体的群体的消失。这个新版本的新颖性是，我们的新条件适用于每个反思性的Banach空间。这种新版本的Garland方法使我们能够在几类Banach空间（均匀弯曲的空间，Hilbertian Spaces和$ L^p $空间）中推断出几种具有系数的组合学标准。使用这些新标准，我们改善了三角模型中随机组的Banach固定点定理的最新结果，并为此类组边界的保形维度提供了急剧的下限。此外，我们针对P-Schatten规范得出了针对群体稳定性的新标准。
We prove a Banach version of Garland's method of proving vanishing of cohomology for groups acting on simplicial complexes. The novelty of this new version is that our new condition applies to every reflexive Banach space. This new version of Garland's method allows us to deduce several criteria for vanishing of group cohomology with coefficients in several classes of Banach spaces (uniformly curved spaces, Hilbertian spaces and $L^p$ spaces). Using these new criteria, we improve recent results regarding Banach fixed point theorems for random groups in the triangular model and give a sharp lower bound for the conformal dimension of the boundary of such groups. Also, we derive new criteria for group stability with respect to p-Schatten norms.
