14 papers
The Coarse Novikov Conjecture for Finite Products of Fibred Coarsely Embeddable Spaces
Liang Guo, Zheng Luo, Qin Wang
In this paper, we prove that the coarse Novikov conjecture holds for finite products of bounded-geometry proper metric spaces whose factors admit fibred coarse embeddings into poss…
The K-theory of maximal and reduced Roe algebras for Hecke pairs with equivariant coarse embeddings
Liang Guo, Hang Wang, Xiufeng Yao
In this paper, we generalize the Dirac-dual-Dirac method to Hecke pairs with equivariant coarse embeddings and establish the K-theoretic isomorphisms between the maximal and reduce…
-theory of ghostly ideals for -coarsely embeddable spaces
Liang Guo, Kang Li, Qin Wang
Ghostly ideals are among the most mysterious objects in coarse index theory. In this paper, we show that if a metric space with bounded geometry admits a coarse embedding into…
Relative higher index theory on quotients of Roe algebras and positive scalar curvature at infinity
Liang Guo, Qin Wang, Chen Zhang
In this paper, we employ quotients of Roe algebras as index containers for elliptic differential operators to study the existence problem of Riemannian metrics with positive scalar…
Geometric Banach property (T) for metric spaces via Banach representations of Roe algebras
Liang Guo, Qin Wang
In this paper, we introduce a notion of geometric Banach property (T) for metric spaces, which jointly generalizes Banach property (T) for groups and geometric property (T) for met…
A nonstanadard analysis approach to limit operators and Fredholmness in Roe-like algebras
Liang Guo, Jin Qian, Qin Wang
Let be a uniformly locally finite metric space, and an operator in the uniform Roe algebra (or uniform quasi-local algebra ). In this paper, we…
Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture
Liang Guo, Qin Wang, Jianchao Wu +1
The equivariant coarse Novikov conjectures stand among a handful profound -theoretic conjectures in noncommutative geometry. Motivated by the quest to verify Novikov-type conjec…
Twisted Roe algebras and their -theory
Jintao Deng, Liang Guo
In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebra…
The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure
Liang Guo, Qin Wang, Chen Zhang
In this paper, we introduce a concept of A-by-FCE coarse fibration structure for metric spaces, which serves as a generalization of the A-by-CE structure for a sequence of group ex…
Higher index theory for spaces with an FCE-by-FCE structure
Jintao Deng, Liang Guo, Qin Wang +1
Let be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of , $(G_n)_{n \…
A coarse geometric approach to the generalised Green-Julg Theorem
Liang Guo, Qin Wang
In this note, we provide a proof of the generalised Green-Julg theorem by using the language of twisted localization algebras introduced by G. Yu. This proof is for those who have…
A Bott periodicity theorem for -spaces and the coarse Novikov conjecture at infinity
Liang Guo, Zheng Luo, Qin Wang +1
We formulate and prove a Bott periodicity theorem for an -space (). For a proper metric space with bounded geometry, we introduce a version of -homol…
Coarse embeddings at infinity and generalized expanders at infinity
Jintao Deng, Liang Guo, Qin Wang +1
We introduce a notion of coarse embedding at infinity into Hilbert space for metric spaces, which is a weakening of the notion of fibred coarse embedding and a far generalization o…
K-theory of the maximal and reduced Roe algebras of metric spaces with A-by-CE coarse fibrations
Liang Guo, Zheng Luo, Qin Wang +1
Let be a discrete metric space with bounded geometry. We show that if admits an "A-by-CE coarse fibration", then the canonical quotient map fro…