Results 41 to 50 of about 409,094 (131)

Weak fuzzy topology on fuzzy topological vector spaces [PDF]

arXiv, 2019
In this paper, we introduce the concept of weak fuzzy linear topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when K (R or C) considered with its usual fuzzy topology.
arxiv  

Simple Models for All Topological Phases [PDF]

arXiv, 2016
We construct simple models for all topological phases of free fermions. These explicit models can realize all the nontrivial topological phases (with any possible topological invariant) of the periodic table. Many well known models for topological insulators and superconductors are special cases of our general constructions.
arxiv  

A note on topological invariants in condensed matter [PDF]

arXiv, 2014
We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time reversal invariant or if there are more phases that has different topological invariants. From a mathematical point
arxiv  

Butterflies and topological quantum numbers [PDF]

arXiv, 2001
The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the topological quantum numbers.
arxiv  

Topological quantum numbers in the Hall effect [PDF]

arXiv, 2003
Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo's formula for the conductance acquires a topological interpretation in terms of Chern numbers and their non-commutative analog, the Fredholm Indices.
arxiv  

Comment on the paper "Does Zeeman's Fine Topology Exist?" at arXiv:1003.3703v1 [PDF]

arXiv, 2011
A constructive and straightforward proof of the existence of the Zeeman topology is provided, contradicting a fallacious claim contained in the paper "Does Zeeman's Fine Topology Exist?" available at arXiv:1003.3703v1.
arxiv  

AKSZ construction of topological open p-brane action and Nambu brackets [PDF]

arXiv, 2011
We review the AKSZ construction as applied to the topological open membranes and Poisson sigma models. We describe a generalization to open topological p-branes and Nambu-Poisson sigma models.
arxiv  

On a Mean Field Theory of Topological 2D Gravity [PDF]

arXiv, 2015
We present a one-dimensional mean field theory for topological 2D gravity. We discuss possible generalizations to other topological field theories, in particular those related to semisimple Frobenius manifolds.
arxiv  

Topological indices in condensed matter [PDF]

arXiv
This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.
arxiv  

Classical mathematical structures within topological graph theory [PDF]

arXiv, 2014
Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some theorems. These are slightly enhanced preparation notes for a talk given at the joint AMS meeting of January 16, 2014 in Baltimore.
arxiv