8 papers
-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…
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…
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…
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…
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…