Embedding products of trees into higher rank

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-30 DOI:10.1112/jlms.70307

Oussama Bensaid, Thang Nguyen

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引用次数: 0

Abstract

We show that there exists a quasi-isometric embedding of the product of $n$ copies of $H_{R}^{2}$ into any symmetric space of non-compact type of rank $n$ , and there exists a bi-Lipschitz embedding of the product of $n$ copies of the 3-regular tree $T_{3}$ into any thick Euclidean building of rank $n$ with co-compact affine Weyl group. This extends a previous result of Fisher–Whyte. The proof is purely geometrical, and the result also applies to the non–Bruhat–Tits buildings.

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将树的乘积嵌入到更高的秩中

我们证明了H $ R $ 2$ \mathbb {H}_{\mathbb {R}}^2$的n$ n$拷贝的乘积在任何秩为n$ n$的非紧型对称空间中存在拟等距嵌入，3正则树T_3$ T_3$的n$个拷贝的乘积存在一个双lipschitz嵌入到任何具有协紧仿射Weyl群的n$ n$秩的厚欧几里得构造中。这扩展了fisher - white先前的结果。证明是纯粹几何的，结果也适用于非bruhat - tits建筑。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.