Higher index theory for spaces with an FCE-by-FCE structure

Jintao Deng; Liang Guo; Qin Wang; Guoliang Yu

doi:10.1016/j.jfa.2024.110679

Higher index theory for spaces with an FCE-by-FCE structure

Jintao Deng
, Liang Guo^*
, Qin Wang
, Guoliang Yu

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

Let (1→N_n→G_n→Q_n→1)_n∈N be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of (N_n)_n∈N, (G_n)_n∈N and (Q_n)_n∈N have bounded geometry. The sequence (G_n)_n∈N is said to have an FCE-by-FCE structure, if the sequence (N_n)_n∈N and the sequence (Q_n)_n∈N admit a fibred coarse embedding into Hilbert space. In this paper, we prove the coarse Novikov conjecture holds for the sequence (G_n)_n∈N with an FCE-by-FCE structure.

Original language	English
Article number	110679
Journal	Journal of Functional Analysis
Volume	288
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2024.110679
State	Published - 1 Jan 2025

Keywords

Coarse Novikov conjecture
K-theory
Operator algebras

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10.1016/j.jfa.2024.110679

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title = "Higher index theory for spaces with an FCE-by-FCE structure",

abstract = "Let (1→Nn→Gn→Qn→1)n∈N be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of (Nn)n∈N, (Gn)n∈N and (Qn)n∈N have bounded geometry. The sequence (Gn)n∈N is said to have an FCE-by-FCE structure, if the sequence (Nn)n∈N and the sequence (Qn)n∈N admit a fibred coarse embedding into Hilbert space. In this paper, we prove the coarse Novikov conjecture holds for the sequence (Gn)n∈N with an FCE-by-FCE structure.",

keywords = "Coarse Novikov conjecture, K-theory, Operator algebras",

author = "Jintao Deng and Liang Guo and Qin Wang and Guoliang Yu",

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year = "2025",

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T1 - Higher index theory for spaces with an FCE-by-FCE structure

AU - Deng, Jintao

AU - Guo, Liang

AU - Wang, Qin

AU - Yu, Guoliang

PY - 2025/1/1

Y1 - 2025/1/1

N2 - Let (1→Nn→Gn→Qn→1)n∈N be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of (Nn)n∈N, (Gn)n∈N and (Qn)n∈N have bounded geometry. The sequence (Gn)n∈N is said to have an FCE-by-FCE structure, if the sequence (Nn)n∈N and the sequence (Qn)n∈N admit a fibred coarse embedding into Hilbert space. In this paper, we prove the coarse Novikov conjecture holds for the sequence (Gn)n∈N with an FCE-by-FCE structure.

AB - Let (1→Nn→Gn→Qn→1)n∈N be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of (Nn)n∈N, (Gn)n∈N and (Qn)n∈N have bounded geometry. The sequence (Gn)n∈N is said to have an FCE-by-FCE structure, if the sequence (Nn)n∈N and the sequence (Qn)n∈N admit a fibred coarse embedding into Hilbert space. In this paper, we prove the coarse Novikov conjecture holds for the sequence (Gn)n∈N with an FCE-by-FCE structure.

KW - Coarse Novikov conjecture

KW - K-theory

KW - Operator algebras

UR - https://www.scopus.com/pages/publications/85204249044

U2 - 10.1016/j.jfa.2024.110679

DO - 10.1016/j.jfa.2024.110679

M3 - 文章

AN - SCOPUS:85204249044

SN - 0022-1236

VL - 288

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

M1 - 110679

ER -

Higher index theory for spaces with an FCE-by-FCE structure

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