Related papers: A geometric view of the Chern character
Given a smooth action of a Lie group on a manifold, we give two constructions of the Chern character of an equivariant vector bundle in the cyclic cohomology of the crossed product algebra. The first construction associates a cycle to the…
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
We use the Chern-Simons action for a SO(3)-connection for the description of point disclinations in the geometric theory of defects. The most general spherically symmetric SO(3)-connection with zero curvature is found. The corresponding…
This paper investigates a variety of coarse homology theories and natural transformations between them. We in particular study the commutativity of a square relating analytical and topological transgressions with algebraic and homotopy…
For a given graph $F$, the $r$-uniform suspension of $F$ is the $r$-uniform hypergraph obtained from $F$ by taking $r-2$ new vertices and adding them to every edge. In this paper, we consider Tur\'{a}n problems on suspension hypergraphs,…
We develop a novel and systematic approach to computing the $(2n-1)$-form Chern-Simons potential given the Pontryagin density, i.e. the $n^{\text{th}}$ Chern character, in arbitrary even dimensions $D=2 n \geq 2$. Throughout we work with a…
In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short/long range interactions through the imaginary time formalism path…
We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their…
Special solutions of string theory in supercritical dimensions can interpolate in time between theories with different numbers of spacetime dimensions (via dimension quenching) and different amounts of worldsheet supersymmetry (via…
In this addendum to our article "Superconnections and Parallel Transport" we give an alternate construction to the parallel transport of a superconnection contained in Corollary 4.4 of \cite{D1}, which has the advantage that is independent…
Recently, Chern vector with arbitrary formula $\textbf{C}\!=\!(\mathcal{C}_{yz},\mathcal{C}_{xz},\mathcal{C}_{xy})$ in three-dimensional systems has been experimentally realized [\B{Nature 609, 925 (2022)}]. Motivated by these progresses,…
Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an…
If $ D \in X$ is a curve with multiple points in a surface, a parabolic bundle defined on $(X;D)$ away from the singularities can be extended in several ways to a parabolic bundle on a resolution of singularities. We investigate the…
The path integral representation for a system of N non-relativistic particles on the plane, interacting through a Chern-Simons gauge field, is obtained from the operator formalism. An effective interaction between the particles appears,…
These theories, which are surely some of the simplest possible quantum field theories, were introduced in a paper of Dijkgraaf and Witten. The path integral reduces to a finite sum, so it is quite amenable to direct mathematical study.…
Let G be a finite group, and let E be a generalised cohomology theory, subject to certain technical conditions. We study a certain ring C(E,G) that is the best possible approximation to E^0BG that can be built using only knowledge of the…
In this paper we introduce the Chern minimal surface in Hermitian surfaces by using the Chern connection, and we show that it only has isolated complex and anticomplex points for a generic one (neither holomorphic nor antiholomorphic). For…
A matter self-interacting model with N=1-supersymmetry in 3D is discussed in connection with the appearance of a central charge in the algebra of the supersymmetry generators. The result is extended to include gauge fields with a…
We give a geometric description of supersymmetric gravity/(non-)abelian $p$-form hierarchies in superspaces with 4D, $N = 1$ super-Poincare invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, $N…
We generalize the framework introduced by Kapustin et al. for doing path integral localization in Chern-Simons theory to work on any Seifert manifold. This is done by topologically twisting the supersymmetric theory considered by Kapustin…