Asymptotic dimension, property A, and Lipschitz maps

被引：0

作者：

M. Cencelj

J. Dydak

A. Vavpetič

机构：

[1] Univerza v Ljubljani,Pedagoška Fakulteta in IMFM

[2] University of Tennessee,Fakulteta za Matematiko in Fiziko

[3] Univerza v Ljubljani,undefined

来源：

Revista Matemática Complutense | 2013年 / 26卷

关键词：

Asymptotic dimension; Coarse geometry; Lipschitz maps; Property A; 54F45; 55M10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

It is well-known that a paracompact space X is of covering dimension n if and only if any map f:X→K from X to a simplicial complex K can be pushed into its n-skeleton K(n). We use the same idea to define dimension in the coarse category. It turns out the analog of maps f:X→K is related to asymptotically Lipschitz maps, the analog of paracompact spaces are spaces related to Yu’s Property A, and the dimension coincides with Gromov’s asymptotic dimension.

引用

页码：561 / 571

页数：10

共 10 条

[1]

Bell G.(2004)On asymptotic dimension of groups acting on trees Geom. Dedic. 103 89-101

[2]

Dranishnikov A.(2008)Hyperbolic dimension of metric spaces St. Petersburg Math. J. 19 67-76

[3]

Buyalo S.(2003)Partitions of unity Topol. Proc. 27 125-171

[4]

Schroeder V.(2008)What is …Property A? Not. Am. Math. Soc. 55 474-475

[5]

Dydak J.(1969)A new proof that metric spaces are paracompact Proc. Am. Math. Soc. 20 603-982

[6]

Nowak P.(1948)Paracompactness and product spaces Bull. Am. Math. Soc. 54 977-240

[7]

Yu G.(2000)The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space Invent. Math. 139 201-undefined

[8]

Rudin M.E.(undefined)undefined undefined undefined undefined-undefined

[9]

Stone A.H.(undefined)undefined undefined undefined undefined-undefined

[10]

Yu G.(undefined)undefined undefined undefined undefined-undefined

← 1 →