Related papers: On spaces with connected Higson coronas

We formulate and study a new coarse (co-)assembly map. It involves a modification of the Higson corona construction and produces a map dual in an appropriate sense to the standard coarse assembly map. The new assembly map is shown to be an…

We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that…

We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact…

Let $G$ be an infinite group, $\kappa$ be an infinite cardinal, $\kappa\leq \mid G\mid$ and let $\mathcal{E}_{\kappa}$ denotes a coarse structure on $G$ with the base $\{\{ (x,y): y\in F x F\}: F\in [G]^{<\kappa}\}$. We prove that if either…

The purpose of this article is to characterize the quasi-isometry type of a proper metric space via the Banach algebra of Higson functions on it.

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…

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…

We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…

We formalize the concept of a family of metric spaces satisfying a coarse property uniformly and we generalize finite decomposition complexity of Erik Guentner, Romain Tessera, and Guoliang Yu. Of particular interest are results determining…

In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a…

We begin the study the algebraic topology of semi-coarse spaces, which are generalizations of coarse spaces that enable one to endow non-trivial `coarse-like' structures to compact metric spaces, something which is impossible in coarse…

We investigate the fixed point property of the group actions on a coarse space and its Higson corona. We deduce the coarse version of Brouwer's fixed point theorem.

This paper presents a new version of boundary on coarse spaces. The space of ends functor maps coarse metric spaces to uniform topological spaces and coarse maps to uniformly continuous maps.

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

We introduce the notion of (hybrid) large scale normal space and prove coarse geometric analogues of Urysohn's Lemma and the Tietze Extension Theorem for these spaces, where continuous maps are replaced by (continuous and) slowly…

Electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology theories. Over the past twenty-five years, a considerable effort has been invested by the computational…

We offer a counterexample to a theorem in the literature and then repair the theorem as follows: The fundamental group of a locally path connected metric space inherits the discrete topology in a natural way if and only if the underlying…

The subpower Higson corona of a proper metric space is defined in \cite{KZ}. We prove that, unlikely to the Higson corona, the closure of a $\sigma$-compact subset of the subpower Higson corona of a proper unbounded metric space does not…

Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…