Related papers: Topological spherical space forms
We establish sharp upper bounds for the topological complexity of motion planning problem in spaces with small fundamental group, i.e. when it is finite of small order or has small cohomological dimension.
I study flux groups of compact symplectic manifolds. Under some topological assumptions, I give a new estimate of the rank of flux groups and give a method of construcion of compact symplectic aspherical manifolds.
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,…
We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we…
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…
We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.
We classify involutions acting on spherical 3-manifolds up to conjugacy. Our geometric approach provides insights into numerous topological properties of these involutions.
We discuss a sufficient condition for a space to be filled with an arbitrary finite number of self-similar spaces using a topological concept.
For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness of centrally symmetric polytopes and the…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.
In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an…
Topological defects are ubiquitous in physics. Whenever a symmetry breaking phase transition occurs, topological defects may form. The best known examples are vortex lines in type II super conductors or in liquid Helium, and declination…
The possibility of obtaining an open set of regular cosmological models is discussed. Cylindrical stiff perfect fluid cosmologies are studied in detail. The condition for geodesic completeness is easy to check. A large family of…
In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.
We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space…