Related papers: Roe functors preserve homotopies

We show that, for uniformly locally finite metric spaces $X$ and $Y$ with isomorphic uniform Roe algebras $C^*_u(X)$ and $C^*_u(Y)$, the existence of a bijective coarse equivalence $f \colon X \to Y$ is equivalent to the injectivity of the…

Let $D, \Omega_1, ..., \Omega_m$ be irreducible bounded symmetric domains. We study local holomorphic maps from $D$ into $\Omega_1 \times... \Omega_m$ preserving the invariant $(p, p)$-forms induced from the normalized Bergman metrics up to…

We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C*-algebra C*(T) associated with it which is a subalgebra of the uniform Roe algebra C*_u(X). We introduce a coarse invariant…

Following Roe and others (see, e.g., [MR1451755]), we (re)develop coarse geometry from the foundations, taking a categorical point of view. In this paper, we concentrate on the discrete case in which topology plays no role. Our theory is…

Gong, Wang and Yu introduced a maximal, or universal, version of the Roe C*-algebra associated to a metric space. We study the relationship between this maximal Roe algebra and the usual version, in both the uniform and non-uniform cases.…

In this paper I show that pointwise bounded asymptotic morphisms between separable metrisable locally convex *-algebras induce continuous maps between the quasi-unitary groups of the algebras, provided that the algebras support a certain…

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 $X$,…

A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…

We study embeddings of uniform Roe algebras which have "large range" in their codomain and the relation of those with coarse quotients between metric spaces. Among other results, we show that if $Y$ has property A and there is an embedding…

We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic $K$-homology and equivariant…

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…

In this thesis we talk about lipschitz-homotopy invariants for manifolds of bounded geometry. There are three main results: the first one is the definition of a controvariant functor between the category of manifolds of bounded geometry…

The structure of the gauge invariant (particle number preserving) C*-algebra generated by the resolvents of a non-relativistic Bose field is analyzed. It is shown to form a dense subalgebra of the bounded inverse limit of a system of…

We propose a quantization of coarse spaces and uniform Roe algebras. The objects are based on the quantum relations introduced by N. Weaver and require the choice of a represented von Neumann algebra. In the case of the diagonal inclusion…

We show that a bounded, linear map between C*-algebras is a weighted $\ast$-homomorphism (the central compression of a $\ast$-homomorphism) if and only if it preserves zero-products, range-orthogonality, and domain-orthogonality. It follows…

For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…

We prove a noncompact version of Haagerup and R{\o}rdam's result about continuous paths of the rotation $C^*$-algebras. It gives a continuous Moyal deformation of Euclidean plane. Moveover, the construction is generalized to noncommutative…

In previous works by the authors, a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back the space of (graded) linear maps between them endowed with a…

We give a structural characterisation of linear operators from one $C^\ast$% -algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a $\ast$-isomorphism, such a map admits of a…

This paper considers homogeneous order preserving continuous maps on the normal cone of an ordered normed vector space. It is shown that certain operators of that kind which are not necessarily compact themselves but have a compact power…