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^*

^*Corresponding author for this work

School of Mathematical Sciences

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

4 Scopus citations

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).

Original language	English
Pages (from-to)	4029-4065
Number of pages	37
Journal	Journal of Functional Analysis
Volume	267
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2014.10.004
State	Published - 1 Dec 2014

Keywords

Coarse geometry
K-theory
Non-positively curved manifolds
The coarse Novikov conjecture

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10.1016/j.jfa.2014.10.004

Cite this

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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",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2014",

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AU - Chen, Xiaoman

AU - Wang, Qin

AU - Wang, Zhijie

PY - 2014/12/1

Y1 - 2014/12/1

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

U2 - 10.1016/j.jfa.2014.10.004

DO - 10.1016/j.jfa.2014.10.004

M3 - 文章

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SN - 0022-1236

VL - 267

SP - 4029

EP - 4065

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 11

ER -

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

Abstract

Keywords

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