Related papers: Characteristic Classes in Computer Algebra

Given a C$^*$-dynamical system $(A, G, \alpha)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \oplus K_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into…

Let X be a Hermitian locally symmetric space. We prove that every Chern class of X has a canonical lift to the cohomology of the Baily- Borel-Satake compactification X* of X and that the resulting Chern numbers satisfy the Hirzebruch…

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…

For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have `geometric K-theory', namely the `transmission algebra' introduced by Boutet de Monvel, the `zero algebra' introduced by Mazzeo and…

We show that the virtual Euler characteristics of the moduli spaces of $s$-pointed algebraic curves of genus $g$ can be determined from a polynomial in $1/\gamma$ where $\gamma$ permits specialization, through $\gamma=1,$ to the complex…

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…

We study constraints on the Chern classes of a vector bundle on a singular variety. We use this constraint to study a variety which carries a Hodge cycle that are not a linear combination of Chern classes of vector bundles on it.

Scheme-theoretic methods are used to classify ternary quadratic forms with values in line bundles over arbitrary schemes and to canonically determine the isomorphisms between them. The association of a quadratic bundle to its even Clifford…

We study the existence of $S^1$-equivariant characteristic classes on certain natural infinite rank bundles over the loop space $LM$ of a manifold $M$. We discuss the different $S^1$-equivariant cohomology theories in the literature and…

Let $X$ be a compact K\"ahler manifold. The set $\cha(X)$ of one-dimensional complex valued characters of the fundamental group of $X$ forms an algebraic group. Consider the subset of $\cha(X)$ consisting of those characters for which the…

In this short review article we sketch some developments which should ultimately lead to the analogy of the Chern-Weil homomorphism for principal bundles in the realm of non-commutative differential geometry. Principal bundles there should…

Let $\mathcal{F}$ be a coherent sheaf on a complex variety $X$ that has a locally free resolution $E^{\bullet}$. In [19], the authors constructed a pseudomeromorphic current whose support is contained in $supp(E^{\bullet})$ that represents…

We show that every bad orbifold vector bundle can be realized as the restriction of a good orbifold vector bundle to a suborbifold of the base space. We give an explicit construction of this result in which the Chen-Ruan orbifold cohomology…

Using the concept of a cohesive module defined by Block, we use the theory of superconnections in the sense of Quillen to construct natural superconnections on Hermitian cohesive modules. By the Chern-Weil construction, we obtain…

We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the automorphism group of the cluster category…

Some cohomology elements, called $\nu$ classes, as a supergeneralization of universal Chern classes, are introduced for canonical super line bundles over $\nu$ projective spaces, a novel supergeometric generalization of projective spaces.…

In this note we use Bott-Borel-Weil theory to compute cohomology of interesting vector bundles on sequences of Grassmanians.

We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte's generalization of the Chern-Weil homomorphism.

Given a matrix factorization, we use the Atiyah class to give an algebraic Chern-Weil type construction to its Chern character; this allows us to realize the Chern character in an explicit way. It also generalizes the existing result to any…

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…