The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space

Xiaoman Chen; Qin Wang; Guoliang Yu

doi:10.1016/j.aim.2013.09.003

The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space

Xiaoman Chen
, Qin Wang
, Guoliang Yu^*

^*此作品的通讯作者

数学科学学院

Fudan University
Texas A&M University

科研成果: 期刊稿件 › 文章 › 同行评审

37 引用（Scopus）

摘要

We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space.

源语言	英语
页（从-至）	88-130
页数	43
期刊	Advances in Mathematics
卷	249
DOI	https://doi.org/10.1016/j.aim.2013.09.003
出版状态	已出版 - 20 12月 2013

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10.1016/j.aim.2013.09.003

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title = "The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space",

abstract = "We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space.",

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N2 - We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space.

AB - We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space.

KW - Coarse Baum-Connes conjecture

KW - Higher index theory

KW - K-theory

KW - Noncommutative geometry

KW - Operator algebras

UR - https://www.scopus.com/pages/publications/84884964277

U2 - 10.1016/j.aim.2013.09.003

DO - 10.1016/j.aim.2013.09.003

M3 - 文章

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SN - 0001-8708

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space

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