连通李群的Assouad-Nagata维数
Assouad-Nagata dimension of connected Lie groups
摘要：
证明了具有左不变黎曼度量的连通李群$G$的渐近Assouad-Nagata维数与其拓扑维数$G/C$一致，其中$C$是极大紧子群.为了证明这一点，我们将计算连通可解李群和半单李群的Assouad-Nagata维数。结果证明了具有字度量的多环群的渐近Assouad-Nagata维数等于它的Hirsch长度，并且某些花环型有限生成群不能与连通李群上的任何余紧格拟等距.
英文摘要：
We prove that the asymptotic Assouad-Nagata dimension of a connected Lie group $G$ equipped with a left-invariant Riemannian metric coincides with its topological dimension of $G/C$ where $C$ is a maximal compact subgroup. To prove it we will compute the Assouad-Nagata dimension of connected solvable Lie groups and semisimple Lie groups. As a consequence we show that the asymptotic Assouad-Nagata dimension of a polycyclic group equipped with a word metric is equal to its Hirsch length and that some wreath-type finitely generated groups can not be quasi-isometric to any cocompact lattice on a connected Lie group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
