Quasi-isometric embeddings of non-uniform lattices
Quasi-isometric embeddings of non-uniform lattices
复制标题
非均匀晶格的准等距嵌入
DOI：
10.4171/cmh/480
复制
发表时间：
2015
影响因子：
0.9
通讯作者：
Thang Nguyen
中科院分区：
文献类型：
--
作者：
D. Fisher;Thang Nguyen
设$G$和$G '$是真实的秩相等且真实的秩至少为$2$的单李群.设$\Gamma <G$和$\Lambda <G '$为非均匀格。我们证明了一个定理，往往意味着任何拟等距嵌入$\Gamma$到$\Lambda$是在有界距离同态。例如，$SL（n，\mathbb Z）$到$SL（n，\mathbb Z[i]）$的任何拟等距嵌入都是在距离同态有界的距离处。我们还包括讨论的一些情况下，这个结果是不正确的什么变成了纯粹的代数原因。
Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $\Gamma <G$ and $\Lambda < G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $\Gamma$ into $\Lambda$ is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of $SL(n,\mathbb Z)$ into $SL(n, \mathbb Z[i])$ is at bounded distance from a homomorphism. We also include a discussion of some cases when this result is not true for what turn out to be purely algebraic reasons.