相关论文: Topological transformation groups

Topological full groups originated from the theory of topological dynamical systems and have been having considerable impact on group theory in recent years. This text represents an introduction/survey on topological full groups. After…

The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.

The purpose of this paper is to present a systematic exposition of the main results obtained in the studies carried out in groupoid theory. Key words and phrases: groupoid, topological groupoid, Lie groupoid, group-groupoid, vector…

We give a characterization of groups with twisted p-periodic cohomology in terms of group actions on mod p homology spheres. An equivalent algebraic characterization of such groups is also presented.

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree…

We describe a new approach towards the systematic construction of finite groups up to isomorphism. This approach yields a practical algorithm for the construction of finite solvable groups up to isomorphism. We report on a GAP…

This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic…

We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these…

We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes. For one type of groups (the toroidal groups), we develop a new…

In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.

In this paper, some generalized metric properties in strongly topological gyrogroups are studied.

This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…

In this paper we discuss the isomorphism types of parabolic subgroups in Kac-Moody groups. The results have applications in the study of topology of Kac-Moody groups and their classifying spaces.

In this paper we have discussed the ideals in Abel Grassmann's groupoids and construct their topologies.

We study topological properties of the graph topology.

We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…

Results about the structure of the set of Egyptian fractions on the line are extended to subsets of topological groups.

In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…

This is a survey of the theory of real trees and their applications.