arXiv research

The paper examines spaces with indecomposable Higson coronae and their properties.

The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional E…

The paper constructs coronas for combable spaces under specific conditions.

The purpose of the paper is to characterize the dimension of sublinear Higson corona $ν_L(X)$ of $X$ in terms of Lipschitz extensions of functions: Theorem: Suppose $(X,d)$ is a proper metric space. The dimension of the sublinear Higson corona $ν_L(X)$ of $X$ is the smallest integer $m\ge 0$ with the following property…

Abstract: Unifies small and large scale geometries using linear algebra concepts.

Maps between metric spaces preserve asymptotic dimension up to a constant.

For a large class of metric space X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension $\dim(ν_L X)$ of the Higson corona of X with respect to the sublinear coarse structure on X. Then we apply this fact to prove the equality AN-asdim(X …

Paper introduces simple coarse structures using equivalence relations on simple ends.

Paper relates asymptotic dimension to cofinal dimension using coarse proximities.

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.

The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic extensional dimension of a proper metric space and extension dimension of its Higson corona.

New maps for large-scale geometry factorize into monotone and light.

This paper is devoted to dualization of dimension-theoretical results from the small scale to the large scale. So far there are two approaches for such dualization: one consisting of creating analogs of small scale concepts and the other amounting to the covering dimension of the Higson corona $ν(X)$ of $X$. The first …

New formulas for coarse indices of twisted operators introduced.

A compact Polish foliated space is considered. Part of this work studies coarsely quasi-isometric invariants of leaves in some residual saturated subset when the foliated space is transitive. In fact, we also use "equi-" versions of this kind of invariants, which means that the definition is satisfied with the same con…

The paper extends end concepts to arbitrary groups and spaces.

The study provides an index for equivariant Callias-type operators and applies it to obstruct positive scalar curvature metrics.

New insights into the structure of blown-up corona of hyperbolic groups.

Unified small and large scale geometry concepts.

Embeds Higson compactification into adelic solenoids.

Interprets coarse symbol and index classes for Callias type operators.

We study a two dimensional analogue of the Roe-Higson index theorem for a partitioned manifold. We prove that Connes' pairing of some invertible element with Roe's cyclic one-cocycle coincides to the Fredholm index of a Toeplitz operator. In the proof of this paper, we use some properties of a circle and use Higson's a…

We show that the rational Novikov conjecture for a group $Γ$ of finite homological type follows from the mod 2 acyclicity of the Higson compactifcation of an E$Γ$. We then show that for groups of finite asymptotic dimension the Higson compactification is mod p acyclic for all p, and deduce the integral Novikov conjectu…

Let $M$ be a complete Riemannian manifold and assume that $M$ is partitioned by a hypersurface $N$. In this paper we introduce a novel class of functions $C_{\mathrm{w}}(M)$ on noncompact manifolds, which is slightly larger than the algebra of Higson functions. Out of $φ$ that belongs to $C_{\mathrm{w}}(M)$ we construc…

Property A was introduced by Yu as a non-equivariant analogue of amenability. Nigel Higson posed the question of whether there is a homological characterisation of property A. In this paper we answer Higson's question affirmatively by constructing analogues of group cohomology and bounded cohomology for a metric space …

The paper studies maps in the Heisenberg group and their images, called Rickman rugs.

This paper extends the C*-signature to non-Witt spaces using noncommutative geometric methods.

In this paper, we give some estimates of the sum of the square norm of the sections of the pluricanonical bundles over a Riemann surface with genus greater than 2 and Gauss curvature (-1). Using these estimate, we give a uniform estimate of the corona problem on Riemann surfaces.

This paper automates mining of COVID-19 scholarly articles using machine learning.

Study weightings from singular Lie filtrations.

In this paper we prove the existence of a natural mapping from the surgery exact sequence for topological manifolds to the analytic surgery exact sequence of N. Higson and J. Roe. This generalizes the fundamental result of Higson and Roe, but in the treatment given by Piazza and Schick, from smooth manifolds to topolog…

We present an alternative approach to the result of Guentner, Higson, and Weinberger concerning the Baum-Connes conjecture for finitely generated subgroups of SL(2,C). Using finite-dimensional methods, we show that the Baum-Connes assembly map for such groups is an isomorphism.

The paper extends higher signature invariants to stratified spaces and establishes a new surgery exact sequence.

The goal is to understand the index-theoretic aspects of the recent preprint of R. Nest and F. Radulescu, math.OA/9911042. The basic observation (due to E. Guenter/N. Higson) is that the index of the Toeplitz operator is equal to the index of an associated Callias type operator, i.e. a Dirac operator with potential, th…

Analytic surgery mapped to homology, leading to new rho numbers and metrics of positive scalar curvature.

Working with group homomorphisms, a construction of manifolds is introduced to preserve homology groups. The construction gives as special cases Qullien's plus construction with handles obtained by Hausmann, the existence of one-sided $h$-cobordism of Guilbault and Tinsley, the existence of homology spheres and higher-…

We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coefficients. This includes as special cases Quillen's plus construction, Bousfield's integral homology localization, the existence of Moore spac…

The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Roe. Our approach makes crucial use of analytic properties and new index theorems for the signature operator on Galois coverings with boundary…

In this paper we state and prove a higher index theorem for an odd-dimensional connected spin riemannian manifold $(M,g)$ which is partitioned by an oriented closed hypersurface $N$. This index theorem generalizes a theorem due to N. Higson and J. Roe in the context of Hilbert modules. Then we apply this theorem to pro…

In the first part of the paper we show how to relate several dimension theories (asymptotic dimension with Higson property, asymptotic dimension of Gromov, and capacity dimension of Buyalo \cite{Buyalo1}) to Nagata-Assouad dimension. This is done by applying two functors on the Lipschitz category of metric spaces: micr…

Defines linear weightings for vector bundles and explores their applications.

We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod $p$ acyclic in the finite dimensional case. Then we give an alternative proof of the Higher Signature Novikov …

Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the concept of asymptotic resemblance as a relation between subsets of a set to define a…

Researchers construct an index map for contact manifolds using K-theory.

We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As a…

In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry. Given a closed spin manifold M with fundamental group G, Stephan Stolz introduced the positive scalar curvature exact sequence, in analogy to the surgery exact sequence in topology. It calculates a structure gr…

Lung segmentation from abnormal CXRs using data imputation.

Study index theory for infinite-dimensional manifolds with LT actions.