相关论文: Group Actions and Covering Maps in the Uniform Cat…

Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…

In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base…

Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions). In this paper we expand the existing framework, so that it will apply to not…

We classify all $\pi_1$-injective proper maps between non-compact surfaces up to proper homotopy.

In this paper, we present a constructive and proof-relevant development of graph theory, including the notion of maps, their faces, and maps of graphs embedded in the sphere, in homotopy type theory. This allows us to provide an elementary…

In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.

We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results…

We develop the notion of a geometric covering of a rigid space X, which yields a much larger class of covering spaces than that studied previously by de Jong. Geometric coverings of X are closed under disjoint unions and are \'etale local…

This is a chapter in a forthcoming book on completely regular codes in distance regular graphs. The chapter provides an overview, and some original results, on codes in distance regular graphs which admit symmetries via a permutation group…

Let R be a compact, connected, orientable surface of genus g with p boundary components. Let C(R) be the complex of curves on R and Mod_R^* be the extended mapping class group of R. Suppose that either g = 2 and p > 1 or g > 2 and p >= 0.…

The purpose of this note is to observe that a homomorphism of discrete groups $f:\Gamma\to G$ arises as the induced map $\pi_0(\mathfrak{M})\to \pi_0(\mathfrak{X})$ on path components of some closed normal inclusion of topological groups…

We develop a theory of group actions and coverings on Brauer graphs that parallels the theory of group actions and coverings of algebras. In particular, we show that any Brauer graph can be covered by a tower of coverings of Brauer graphs…

The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…

We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.

We give a short proof that, for nice $X$, the based fundamental groupoid of $X$ with topology induced by the compact open topology on the space of paths, is indeed the universal covering space of $X$.

We show that a finitely generated group of analytic diffeomorphisms that is expanding and locally discrete in the analytic category is analytically conjugate to a uniform lattice of a finite covering of the group of projective maps of the…

Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

In this paper we develop analysis of the monopole maps over the universal covering space of a compact four manifold. We induce a property on local properness of the covering monopole map under the condition of closeness of the AHS complex.…

We define the action of a locally compact group $G$ on a topological graph $E$. This action induces a natural action of $G$ on the $C^*$-correspondence ${\mathcal H}(E)$ and on the graph $C^*$-algebra $C^*(E)$. If the action is free and…