Related papers: Some remarks about homeomorphisms, "energy", and s…
In this article, we will give a brief introduction to the topological insulators. We will briefly review some of the recent progresses, from both theoretical and experimental sides. In particular, we will emphasize the recent progresses…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
This article is a short survey of the history of functional analysis for topologists.
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…
Physics of dielectric mixtures are presented to stimulate discussion and to provide information on the recent advances in this topic.
This is an expository article about the topological theory of digital images, and a gamification of a research project.
We explore whether the topology of energy landscapes in chemical systems obeys any rules and what these rules are. To answer this and related questions we use several tools: (i)Reduced energy surface and its density of states, (ii)…
A reduction of properties (invariants) of compact sets of real numbers to properties of countable orders is presented here. Discussed here is also an embedding property of some compact sets that are called t$\mathbb R$-sets. Among others,…
We survey some properties of homotopical and homological $Z_n$-sets in topological spaces.
Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topological space connects the two types of topological…
This article surveys gauge theory for families and its applications to the comparison between the diffeomorphism group and the homeomorphism group of $4$-manifolds, up to 2021.
Sec I - Introduction Sec II - Equilibrium properties: generalities and methodology Sec III - Equilibrium properties: some important quantities Sec IV - Dynamical properties: heuristic approach Sec V - Dynamical properties: stochastic…
Let $N=(\Omega,\sigma)$ and $M=(\Omega^*,\rho)$ be doubly connected Riemann surfaces and assume that $\rho$ is a smooth metric with bounded Gauss curvature $\mathcal{K}$ and finite area. The paper establishes the existence of homeomorphisms…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We review measures of street network structure proposed in the recent literature, establish their relevance to practice, and identify open challenges facing researchers. These measures' empirical values vary substantially across world…
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
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…