Compression of uniform embeddings into Hilbert space

被引：7

作者：

Brodskiy, N. ^{[1
]}

Sonkin, D. ^{[2
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Univ Virginia, Dept Math, Charlottesville, VA 22903 USA

来源：

TOPOLOGY AND ITS APPLICATIONS | 2008年 / 155卷 / 07期

基金：

美国国家科学基金会;

关键词：

uniform embedding; Hilbert space compression; hyperbolic group; CAT(0) cubical complex;

D O I：

10.1016/j.topol.2007.12.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If one tries to embed a metric space uniformly in Hilbert space, how close to quasi-isometric could the embedding be? We answer this question for finite dimensional CAT(0) cube complexes and for hyperbolic groups. In particular, we show that the Hilbert space compression of any hyperbolic group is 1. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：725 / 732

页数：8

共 17 条

[1]

ARZHANTSEVA GN, MATHGR0411605

[2] Embeddings of Gromov hyperbolic spaces [J].