Related papers: Open Cones and $K$-theory for $\ell^p$ Roe Algebra…

In this paper, we verify the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension for $p\in[1,\infty)$. We also show that the $K$-theory of $L^p$ Roe algebras are independent of $p\in(1,\infty)$ for spaces with…

We prove an $\ell^p$-version of the coarse Baum-Connes conjecture for spaces that coarsely embedds into $\ell^q$-spaces for any $p$ and $q$ in $[1,\infty)$.

In this paper, we characterize when the $\ell^p$ uniform Roe algebra of a metric space with bounded geometry is (stably) finite and when it is properly infinite in standard form for $p\in [1,\infty)$. Moreover, we show that the $\ell^p$…

We consider an $\ell^p$ coarse Baum-Connes assembly map for $1<p<\infty$, and show that it is not surjective for expanders arising from residually finite hyperbolic groups.

In this paper, we investigate the $L^{p}$ coarse Baum-Connes conjecture for $p\in [1,\infty)$ via $C_{0}$ coarse structure, which is a refinement of the bounded coarse structure on a metric space. We prove that the $C_{0}$ version of the…

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras.…

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 algebras, including a coarse analogue of the imprimitivity theorem…

We introduce the notion of (strong) subexponential growth for \'etale groupoids and study its basic properties. In particular, we show that the K-groups of the associated groupoid $L^p$-operator algebras are independent of $p \in…

We formulate and prove a Bott periodicity theorem for an $\ell^p$-space ($1\leq p<\infty$). For a proper metric space $X$ with bounded geometry, we introduce a version of $K$-homology at infinity, denoted by $K_*^{\infty}(X)$, and the Roe…

In this paper, we connect the rigidity problem and the coarse Baum-Connes conjecture for Roe algebras. In particular, we show that if $X$ and $Y$ are two uniformly locally finite metric spaces such that their Roe algebras are…

We investigate the rigidity of the $\ell^p$ analog of Roe-type algebras. In particular, we show that if $p\in[1,\infty)\setminus\{2\}$, then an isometric isomorphism between the $\ell^p$ uniform Roe algebras of two metric spaces with…

Given a metric space with bounded geometry, one may associate with it the $\ell^p$ uniform Roe algebra and the $\ell^p$ uniform algebra, both containing information about the large scale geometry of the metric space. We show that these two…

We prove the Baum--Connes conjecture with arbitrary coefficients for some classes of groups: (1) Linear algebraic groups over a non-archimedean local field. (2) Linear algebraic groups over the adeles of a global field k, provided that at…

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 curvature on non-compact complete Riemannian manifolds. The…

We investigate Banach algebras of convolution operators on the $L^p$ spaces of a locally compact group, and their K-theory. We show that for a discrete group, the corresponding K-theory groups depend continuously on $p$ in an inductive…

Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups, or equivalently, for certain reduced partial crossed products. In the case of…

In this paper, we compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces in terms of those of each of the components. The (co)homology theories we consider are, $K$-theory, Alexander-Spanier…

We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boundaries. As an application, we show that such spaces satisfy…

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the…

Let $X$ be a discrete metric space with bounded geometry. We show that if $X$ admits an "A-by-CE coarse fibration", then the canonical quotient map $\lambda: C^*_{\max}(X)\to C^*(X)$ from the maximal Roe algebra to the Roe algebra of $X$,…