论文标题
在可融合组的粗嵌入中
On coarse embeddings of amenable groups into hyperbolic graphs
论文作者
论文摘要
在本说明中，我们证明，如果有限生成的Amenable组将普通的地图接收到双曲线空间和欧几里得空间的直接乘积，那么它几乎必须是nilpotent。我们推断出一个可正约的群体会定期嵌入双曲线群体，并且仅当它实际上是nilpotent时，回答了休ume和sisto的问题。我们描述了由于查尔斯·弗朗西斯（Charles Frances）引起的洛伦兹几何形状的应用。
In this note we prove that if a finitely generated amenable group admits a regular map to a direct product of a hyperbolic space and a euclidean space, then it must be virtually nilpotent. We deduce that an amenable group regularly embeds into a hyperbolic group if and only if it is virtually nilpotent, answering a question of Hume and Sisto. We describe an application to Lorentz geometry due to Charles Frances.
