11 citations · 33 across the 23 of their papers we have counts for
23 papers
-Theoretic Comparison of Roe and Quasi-Local Algebras via Projections
Kang Li, Jiawen Zhang, Jingming Zhu
A central question in higher index theory and operator algebras is whether the Roe algebra and the quasi-local algebra associated with a metric space of bounded geometry coincide,…
Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity
Qizheng You, Jiawen Zhang
In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying the Gromov's -point condition) while the intersection of any two met…
Rigidity for geometric ideals in uniform Roe algebras
Baojie Jiang, Jiawen Zhang
In this paper, we investigate the rigidity problems for geometric ideals in uniform Roe algebras associated to discrete metric spaces of bounded geometry. These ideals were introdu…
Ghostly ideals in uniform Roe algebras
Qin Wang, Jiawen Zhang
In this paper, we investigate the ideal structure of uniform Roe algebras for general metric spaces beyond the scope of Yu's property A. Inspired by the ideal of ghost operators co…
Characterisations for uniform amenability
Jingming Zhu, Jiawen Zhang
In this paper, we provide several characterisations for uniform amenability concerning a family of finitely generated groups. More precisely, we show that the Hulanicki-Reiter cond…
The equivariant coarse Baum-Connes conjecture for actions by a-T-menable groups
Benyin Fu, Jiawen Zhang
The equivariant coarse Baum-Connes conjecture was firstly introduced by Roe [29] as a unified way to approach both the Baum-Connes conjecture and its coarse counterpart. In this pa…
The strongly quasi-local coarse Novikov conjecture and Banach spaces with Property (H)
Xiaoman Chen, Kun Gao, Jiawen Zhang
In this paper, we introduce a strongly quasi-local version of the coarse Novikov conjecture, which states that certain assembly map from the coarse -homology of a metric space t…
Strongly Quasi-local algebras and their -theories
Hengda Bao, Xiaoman Chen, Jiawen Zhang
In this paper, we introduce a notion of strongly quasi-local algebras. They are defined for each discrete metric space with bounded geometry, and sit between the Roe algebra and th…
Measured expanders
Kang Li, Ján Špakula, Jiawen Zhang
By measured graphs we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincaré ine…
Measured asymptotic expanders and rigidity for Roe algebras
Kang Li, Ján Špakula, Jiawen Zhang
Our main result about rigidity of Roe algebras is the following: if and are metric spaces with bounded geometry such that their Roe algebras are -isomorphic, then an…
A Markovian and Roe-algebraic approach to asymptotic expansion in measure
Kang Li, Federico Vigolo, Jiawen Zhang
In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a machinery of Markov expansion and ob…
Asymptotic expansion in measure and strong ergodicity
Kang Li, Federico Vigolo, Jiawen Zhang
In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalises expansion in measure and provides a new perspective on th…
On the structure of asymptotic expanders
Ana Khukhro, Kang Li, Federico Vigolo +1
In this paper, we use geometric tools to study the structure of asymptotic expanders and show that a sequence of asymptotic expanders always admits a "uniform exhaustion by expande…
Quasi-local Algebras and Asymptotic Expanders
Kang Li, Piotr Nowak, Ján Špakula +1
In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introd…
Limit operator theory for groupoids
Kyle Austin, Jiawen Zhang
We extend the symbol calculus and study the limit operator theory for -compact, étale and amenable groupoids, in the Hilbert space case. This approach not only unifies various e…
Quasi-Locality and Property A
Ján Špakula, Jiawen Zhang
Let be a metric space with bounded geometry, , and let be a Banach space. The main result of this paper is that either if has Yu's Property A…
Extreme cases of limit operator theory on metric spaces
Jiawen Zhang
The theory of limit operators was developed by Rabinovich, Roch and Silbermann to study the Fredholmness of band-dominated operators on for $p \in \{0\} \cup…
A quasi-local characterisation of -Roe algebras
Kang Li, Zhijie Wang, Jiawen Zhang
Very recently, Špakula and Tikuisis provide a new characterisation of (uniform) Roe algebras via quasi-locality when the underlying metric spaces have straight finite decomposition…
Coarse median algebras: The intrinsic geometry of coarse median spaces and their intervals
Graham A. Niblo, Nick Wright, Jiawen Zhang
This paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a si…
A four point characterisation for coarse median spaces
Graham A. Niblo, Nick Wright, Jiawen Zhang
Coarse median spaces simultaneously generalise the classes of hyperbolic spaces and median algebras, and arise naturally in the study of the mapping class groups and many other con…
A characterization for asymptotic dimension growth
Goulnara Arzhantseva, Graham A. Niblo, Nick Wright +1
We give a characterization for asymptotic dimension growth. We apply it to CAT(0) cube complexes of finite dimension, giving an alternative proof of N. Wright's result on their fin…
Large scale properties for bounded automata groups
Xiaoman Chen, Jiawen Zhang
In this paper, we study some large scale properties of the mother groups of bounded automata groups. First we give two methods to prove every mother group has infinite asymptotic d…
Equi-variant and Stable Finite Decomposition Complexity
Jiawen Zhang
In this paper, we introduce and study various kinds of decomposition complexity. First, we give a characterization of residually finite groups having finite decomposition complexit…