Metric sparsification and operator norm localization

Xiaoman Chen; Romain Tessera; Xianjin Wang; Guoliang Yu

doi:10.1016/j.aim.2008.03.016

Metric sparsification and operator norm localization

Xiaoman Chen
, Romain Tessera
, Xianjin Wang
, Guoliang Yu

Fudan University
Vanderbilt University

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

36 Citations (Scopus)

Résumé

We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. In particular, we introduce a sufficient geometric condition (called metric sparsification) for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that a sequence of expanding graphs does not possess the operator norm localization property.

langue originale	Anglais
Pages (de - à)	1496-1511
Nombre de pages	16
journal	Advances in Mathematics
Volume	218
Numéro de publication	5
Les DOIs	https://doi.org/10.1016/j.aim.2008.03.016
état	Publié - 1 août 2008
Modification externe	Oui

Accès au document

10.1016/j.aim.2008.03.016

Contient cette citation

@article{9e8420535aa848b3afe7f968bfba4ba1,

title = "Metric sparsification and operator norm localization",

abstract = "We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. In particular, we introduce a sufficient geometric condition (called metric sparsification) for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that a sequence of expanding graphs does not possess the operator norm localization property.",

keywords = "Metric sparsification, Novikov conjecture, Operator K-theory, Operator norm localization",

author = "Xiaoman Chen and Romain Tessera and Xianjin Wang and Guoliang Yu",

year = "2008",

month = aug,

day = "1",

doi = "10.1016/j.aim.2008.03.016",

language = "English",

volume = "218",

pages = "1496--1511",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "5",

}

TY - JOUR

T1 - Metric sparsification and operator norm localization

AU - Chen, Xiaoman

AU - Tessera, Romain

AU - Wang, Xianjin

AU - Yu, Guoliang

PY - 2008/8/1

Y1 - 2008/8/1

N2 - We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. In particular, we introduce a sufficient geometric condition (called metric sparsification) for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that a sequence of expanding graphs does not possess the operator norm localization property.

AB - We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. In particular, we introduce a sufficient geometric condition (called metric sparsification) for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that a sequence of expanding graphs does not possess the operator norm localization property.

KW - Metric sparsification

KW - Novikov conjecture

KW - Operator K-theory

KW - Operator norm localization

U2 - 10.1016/j.aim.2008.03.016

DO - 10.1016/j.aim.2008.03.016

M3 - Article

AN - SCOPUS:44249102046

SN - 0001-8708

VL - 218

SP - 1496

EP - 1511

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 5

ER -

Metric sparsification and operator norm localization

Résumé

Accès au document

Empreinte digitale

Contient cette citation