Related papers: Relative Chern character number and super-connecti…

For two complex vector bundles admitting a homomorphism with isolated singularities between them, we establish a Poincar\'e-Hopf type formula for the difference of the Chern character numbers of these two vector bundles. As a consequence,…

The Chern character of a complex vector bundle is most conveniently defined as the exponential of a curvature of a connection. It is well known that its cohomology class does not depend on the particular connection chosen. It has been shown…

These notes form the next episode in a series of articles dedicated to a detailed proof of a cohomological index formula for transversally elliptic pseudo-differential operators and applications. The first two chapters are already available…

Coherent sheaves on general complex manifolds do not necessarily have resolutions by finite complexes of vector bundles. However D. Toledo and Y.L.L. Tong showed that one can resolve coherent sheaves by objects analogous to chain complexes…

When the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the $K-$theory index. This result gives a concrete connection…

Combinatorial ideas are developed in this article to study Chern numbers on ample and numerically effective vector bundles. An effective lower bound for Chern numbers of ample vector bundles is established, which makes some progress towards…

We provide a formula for the Chern character of a holomorphic vector bundle in the hyper-cohomology of the de Rham complex of holomorphic sheaves on a complex manifold. This Chern character can be thought of as a completion of the Chern…

In this paper, complex vector bundles of rank $r$ over $8$-dimensional spin$^{c}$ manifolds are classified in terms of the Chern classes of the complex vector bundles and the cohomology ring of the manifolds, where $r = 3$ or $4$. As an…

We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These densities are analogues of the Chern forms of a complex…

Given a vector bundle $E$, we give an explicit formula to compute Chern classes of Schur bundles $\operatorname{S}^\alpha E$ in terms of those of $E$.

Using the theory of quantized equivariant vector bundles over compact coadjoint orbits we determine the Chern characters of all noncommutative line bundles over the fuzzy sphere with regard to its derivation based differential calculus. The…

Here we are fixing an output of a trivial calculation based on Konsevich's differential 2-form for the Chern class of polygon bundle. As a result an interesting combinatorics and arithmetics jumps right out of a jukebox. The calculation…

A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…

We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the construction of a twist functor for…

First we make a brief review of coherent states and prove that the resolution of unity can be obtained by the 1-st Chern character of some bundle. Next we define a Grassmann manifold for a set of coherent states and construct the pull-back…

Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…

We exhaustively classify topological equivariant complex vector bundles over two-sphere under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most)…

It is known that Chern characteristic numbers of compact complex manifolds cannot have arbitrary values. They satisfy certain divisability conditions. W. Ebeling and S. M. Gusein-Zade gave a definition of Chern characteristic numbers of…

We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in…

We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum…