Related papers: The Index of discontinuous Vector Fields: Topologi…
By demanding that the path integral measure of topological field theories be metric independent, we can derive powerful constraints on the particle content of a topological field theory as well as on the dimensionality of space-time.
Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane non-smooth vector fields can be chaotic, a…
An intersection of sets $A = \bigcap_{i \in I}B_i$ is irredundant if no $B_i$ can be omitted from this intersection. We develop a topological approach to irredundance by introducing a notion of a spectral representation, a spectral space…
Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…
The difficulties with which the concept of point-like particles is beset, such as the infinities encountered in the existing theories of elementary particles, suggest a different approach to the study of these particles. Instead of…
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the…
We give a global geometric decomposition of continuously differentiable vector fields on $\mathbb{R}^n$. More precisely, given a vector field of class $\mathcal{C}^{1}$ on $\mathbb{R}^{n}$, and a geometric structure on $\mathbb{R}^n$, we…
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order…
Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of…
A once-extended d-dimensional topological field theory Z is a symmetric monoidal functor (taking values in a chosen target symmetric monoidal (infty,2)-category) assigning values to (d-2)-manifolds, (d-1)-manifolds, and d-manifolds. We show…
Topological insulators are a new class of materials that have engendered considerable research interest among the condensed matter community owing primarily to their application prospects in quantum computations and spintronics. Many of the…
Magnetic nulls are locations where the magnetic field vanishes. Nulls are the location of magnetic reconnection, and they determine to a large degree the magnetic connectivity in a system. We describe a novel approach to understanding…
We classify, up to a natural equivalence relation, vector fields of the plane which belong to the kernel of a 1--form. This form can be closed, in which case the vector fields are integrable, or not, in which case the differential of the…
The topological vertex is a universal series which can be regarded as an object in combinatorics, representation theory, geometry, or physics. It encodes the combinatorics of 3D partitions, the action of vertex operators on Fock space, the…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…
Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have…
For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a…
The relative motion of material, point-like observers is analysed in terms of coordinate maps between the respective rest-frame of each observer. Under the assumption these maps are $C^{2}$-regular, conservation laws are deduced, which in…
We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of…