亚线性 Bilipschitz 同胚与可解李群的准几何分类
群论
2026-02-17 v3
摘要
我们证明了亚线性 Bilipschitz 同胚的乘积定理，这概括了 Kapovich、Kleiner 和 Leeb 关于积空间准几何等距的经典工作。我们运用我们的乘积定理来区分具有相同维数、锥维数和 Dehn 函数的可解群家族；实际上我们通过区分它们在亚线性 Bilipschitz 同胚下的情况来实现这一点，这稍强于准几何等距。作为一个应用，我们恢复了 Bourdon 和 Rémy 使用不同群体最近获得的事实，即存在不可数多个 indecomposable、non-unimodular、high rank 可解李群的准几何等距类。
引用
@article{arxiv.2410.05042,
title = {Sublinear Bilipschitz Equivalence and the Quasiisometric Classification of Solvable Lie Groups},
author = {Ido Grayevsky and Gabriel Pallier},
journal= {arXiv preprint arXiv:2410.05042},
year = {2026}
}
备注
v1->v2: v1 has been split in two parts. v2 contains the first part, after revision and the addition of Corollary D. The second part of v1 can be found at arXiv:2509.12823. v2->v3: Revised following a referee report, corrections in Section 2 and weakening of the claim about the error term in the conclusion of Theorem A