Related papers: Gauss-Bonnet-Chern theorem and differential charac…

For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…

We describe Cheeger-Simons differential characters in terms of a variant of Turaev's homotopy quantum field theories based on chains in a smooth manifold X.

For two complex vector bundles admitting a homomorphism, whose singularity locates in the disjoint union of some odd--dimensional spheres, we give a formula to compute the relative Chern characteristic number of these two complex vector…

We begin by explaining how a physical problem of studying the quantum Hall effect on a closed surface $C$ leads, via Laughlin's approach, to a mathematical question of describing the rank and the first Chern class of a particular vector…

Using a nonlinear version of the tautological bundle over Gra{\ss}mannians, we construct a transgression map for differential characters from $M$ to the nonlinear Gra{\ss}mannians $\mathrm{Gr}^S(M)$ of submanifolds of $M$ of a fixed type…

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…

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,…

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 prove that Schur polynomials in Chern forms of Nakano and dual Nakano positive vector bundles are positive as differential forms. Moreover, modulo a statement about the positivity of a "double mixed discriminant" of linear operators on…

For any (n-1)-dimensional simplicial complex, we construct a particular n-dimensional complex vector bundle over the associated Davis-Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the…

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

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…

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…

Absolutely indecomposable vector bundle and parabolic vector bundles are well-studied via quiver representations. In this paper, we study absolutely indecomposable quasi-parabolic $G$-bundles over $\mathbb{P}^1$ with generic additive…

Type families on higher inductive types such as pushouts can capture homotopical properties of differential geometric constructions including connections, curvature, and vector fields. We define a class of pushouts based on simplicial…

In Proc Math Sci 129, 70(219), Rakesh Pawar considers and solves a certain extension problem. In this note, we observe that the existence and uniqueness of differential characters (defined as objects which fit into a hexagon diagram) follow…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…

We prove that a vector bundle $\pi : E \to M$ is characterized by the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of…

A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…