Related papers: Introduction to Kundt spaces
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
We discuss domestic affairs of metric spaces, keeping away from any extra structure. Topics include universal spaces, injective spaces, Hausdorff and Gromov--Hausdorff convergences, and ultralimits.
This is an exposition of homotopical results on the geometric realization of semi-simplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The…
This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a…
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…
We introduce the notion of the "covering type" of a space, which is more subtle that the notion of Lusternik Schnirelman category. It measures the complexity of a space which arises from coverings by contractible subspaces whose non-empty…
We introduce two notions of coarse embeddability between operator spaces: almost complete coarse embeddability of bounded subsets and spherically-complete coarse embeddability. We provide examples showing that these notions are strictly…
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…
The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted…
We give a definition of compactness in L-fuzzy topological spaces and provide a characterization of compact L-fuzzy topological spaces, where L is a complete quasi-monoidal lattice with some additional structures, and we present a version…
We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.
These lecture notes from a first course in algebraic topology use the fundamental group and orbit categories to classify covering spaces.
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
Classical geometry of de Sitter spacetime is reviewed in arbitrary dimensions. Topics include coordinate systems, geodesic motions, and Penrose diagrams with detailed calculations.
Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…
The aim of this paper is to provide a gentle introduction to Chabauty topology, while very little background knowledge is assumed. As an example, we provide pictures for the Chabauty space of C*. Note that the description of this space is…
In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of…
These lectures are a brief introduction to supersymmetry.
We introduce conformal anti-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a conformal submersion and find…
The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…