Related papers: Topological Structures in the Standard Model at Hi…
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.
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
On objects of a triangulated category with a stability condition, we construct a topology.
The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these "higher-order" boundary states…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
We outline the basic ideas of the topological mechanisms of superconductivity. A gauged model of correlated electronic system where a topological fluid is formed as a result of a strong interaction is discussed.
The author explains local and global model structures on higher orbifolds which are truncated \'{e}tale differentiable higher stacks, and discuss the application of the model structures to quantum cohomology of higher and derived orbifolds.
We study topological properties of the graph topology.
Topological properties of the gauge field in a two-dimensional Higgs model are investigated. Results of exploratory numerical simulations are presented.
We survey some properties of homotopical and homological $Z_n$-sets in topological spaces.
We study some topological properties of attractors.
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
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 give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…
Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…
Topological characterization of torus groups is given.
In this paper we have discussed the ideals in Abel Grassmann's groupoids and construct their topologies.