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

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1496-1511
Number of pages	16
Journal	Advances in Mathematics
Volume	218
Issue number	5
DOIs	https://doi.org/10.1016/j.aim.2008.03.016
Publication status	Published - 1 Aug 2008
Externally published	Yes

Keywords

Metric sparsification
Novikov conjecture
Operator K-theory
Operator norm localization

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10.1016/j.aim.2008.03.016

Cite this

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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.",

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AU - Chen, Xiaoman

AU - Tessera, Romain

AU - Wang, Xianjin

AU - Yu, Guoliang

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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

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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

Abstract

Keywords

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