Related papers: Topological characterization of torus groups

The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.

Higher order group cohomology is defined and first properties are given. Using modular symbols, an Eichler-Shimura homomorphism is constructed mapping spaces of higher order cusp forms to higher order cohomology groups.

For each subcomplex of the standard CW-structure on any torus, we compute the homology of a certain infinite cyclic regular covering space. In all cases when the homology is finitely generated, we also compute the cohomology ring. For…

The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.

We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…

An upper bound is obtained on the rank of a torus which can act smoothly and effectively on a smooth, closed, simply connected, rationally elliptic manifold. In the maximal-rank case, the manifolds admitting such actions are classified up…

This paper extends the study of group algebras of finite groups in which the socle of the center is an ideal. We provide a detailed analysis of the structure of these groups. In a particular case, we reach a complete characterization of the…

A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…

In this short note we give a characterization of ZM-groups that uses the functions defined and studied in [3,4]. This leads to a proof of Conjecture 6 in [4].

This article gives a conceptual introduction to the topos approach to the formulation of physical theories.

In this note, we investigate some topological properties of probabilistic modular spaces.

We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.

[Note to the reader: properties (C2) and (C2)* are under development, in order to form a generalization of (C3) and (C3)*]

In this paper, we construct a comparison map from the topological fundamental group to the pro-\'etale fundamental group for a complex variety.

In this paper it is demonstrated that the Kasparov pairing is continuous with respect to the natural topology on the Kasparov groups, so that a KK-equivalence is an isomorphism of topological groups. In addition, we demonstrate that the…

We establish a bi-equivalence between the bi-category of topoi with enough points and a localisation of a bi-subcategory of topological groupoids

A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings. A number of classical, as well as some new results about…

In this paper, we obtain classification of the topological holonomy groups in $SO(3)$. Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by…

We characterise gaps in the full homomorphism order of graphs.

This paper is a survey on the Lickorish type construction of some kind of closed manifolds over simple convex polytopes. Inspired by Lickorish's theorem, we propose a method to describe certain families of manifolds over simple convex…