Fibred coarse embedding into non-positively curved manifolds and higher index problem

Xiaoman Chen; Qin Wang; Zhijie Wang

doi:10.1016/j.jfa.2014.10.004

Fibred coarse embedding into non-positively curved manifolds and higher index problem

Xiaoman Chen
, Qin Wang
, Zhijie Wang^*

^*此作品的通讯作者

数学科学学院

Fudan University
Jiaxing University

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

Let X={big square union}n=1∞Xn be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry. In this paper, we show that the coarse Novikov conjecture holds for X, if X admits a fibred coarse embedding into a simply connected complete Riemannian manifold of non-positive sectional curvature. This includes a large class of expander graphs with geometric property (T).

源语言	英语
页（从-至）	4029-4065
页数	37
期刊	Journal of Functional Analysis
卷	267
期	11
DOI	https://doi.org/10.1016/j.jfa.2014.10.004
出版状态	已出版 - 1 12月 2014

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title = "Fibred coarse embedding into non-positively curved manifolds and higher index problem",

abstract = "Let X=\{big square union\}n=1∞Xn be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry. In this paper, we show that the coarse Novikov conjecture holds for X, if X admits a fibred coarse embedding into a simply connected complete Riemannian manifold of non-positive sectional curvature. This includes a large class of expander graphs with geometric property (T).",

keywords = "Coarse geometry, K-theory, Non-positively curved manifolds, The coarse Novikov conjecture",

author = "Xiaoman Chen and Qin Wang and Zhijie Wang",

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AU - Wang, Qin

AU - Wang, Zhijie

PY - 2014/12/1

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N2 - Let X={big square union}n=1∞Xn be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry. In this paper, we show that the coarse Novikov conjecture holds for X, if X admits a fibred coarse embedding into a simply connected complete Riemannian manifold of non-positive sectional curvature. This includes a large class of expander graphs with geometric property (T).

AB - Let X={big square union}n=1∞Xn be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry. In this paper, we show that the coarse Novikov conjecture holds for X, if X admits a fibred coarse embedding into a simply connected complete Riemannian manifold of non-positive sectional curvature. This includes a large class of expander graphs with geometric property (T).

KW - Coarse geometry

KW - K-theory

KW - Non-positively curved manifolds

KW - The coarse Novikov conjecture

UR - https://www.scopus.com/pages/publications/84908218766

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JO - Journal of Functional Analysis

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Fibred coarse embedding into non-positively curved manifolds and higher index problem

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