Related papers: Generalized Universal Covers of Uniform Spaces

In this paper, we generalize the defining equation for de Sitter space by replacing the de Sitter radius with a function $f$ satisfying certain conditions; each resulting hypersurface is diffeomorphic to de Sitter space, and has a geometry…

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of…

This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…

In this paper author proposes a construction of a universal space of type $K(\pi,1)$ such that any action (up to homotopy conjugation) of a given finite group $G$ on spaces of the same homotopy type is presented on the constructed space.…

We study the geometry of universal embedding spaces for compact almost complex manifolds of a given dimension. These spaces are complex algebraic analogues of twistor spaces that were introduced by J-P. Demailly and H. Gaussier. Their…

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic…

Consider a finite, regular cover $Y\to X$ of finite graphs, with associated deck group $G$. We relate the topology of the cover to the structure of $H_1(Y;\mathbb{C})$ as a $G$-representation. A central object in this study is the {\em…

In this paper, we have obtained a generalization of the Grothendieck's theorem for the space of continuous mappings $C_{\lambda,\mu}(X,Y)$ where $Y$ is a complete uniform space with the uniformity $\mu$ endowed with the topology of uniform…

Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…

We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented…

We study notions of persistent homotopy groups of compact metric spaces together with their stability properties in the Gromov-Hausdorff sense. We pay particular attention to the case of fundamental groups, for which we obtain a more…

The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the…

Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…

In this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to $M \times [0, \infty)$ where $M$ is a closed Euclidean manifold. These are classified in [2]. The marked moduli space is…

We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.

Pulling back complex structures along a branched covering induces a holomorphic isometric embedding of Teichm\"uller spaces. We show that for dimension at least $2$, all isometric embeddings arise from branched coverings. This generalizes a…

Let $U$ be a finite dimentional vector space over $\mathbb R$ or $\mathbb C$, and let $\rho:G\to GL(U)$ be a representation of a connected Lie group $G$. A linear subspace $V\subset U$ is called universal if every orbit of $G$ meets $V$. We…

In the theory of crossed modules, considering arbitrary self-actions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of generalized crossed module emerges. In this paper we give a…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…