Related papers: On transgression in associated bundles

We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal $G$-bundle $Q$ over a manifold $X$, including the case of the gauge group of $Q$. These results are used to define…

In this paper, we give a simple proof of the Gauss-Bonnet-Chern theorem for a real oriented Finsler vector bundle with rank equal to the dimension of the base manifold. As an application, a Gauss-Bonnet-Chern formula for any…

The $\bar{\partial}_{_{J}}$ operator over an almost complex manifold induces canonical connections of type $(0,1)$ over the bundles of $(p,0)$-forms. If the almost complex structure is integrable then the previous connections induce the…

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…

We provide an intersection-theoretic formula for the Euler characteristic of the moduli space of smooth curves. This formula reads purely in terms of Hodge integrals and, as a corollary, the standard calculus of tautological classes gives a…

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 we study deformations of $C^*$-algebras that are given as cross-sectional $C^*$-algebras of Fell bundles over locally compact groups $G$. Our deformation comes from a direct deformation of the Fell bundles via certain…

We prove a formula for the multiplication of equivariant first Chern classes of tautological bundles of type A bow varieties with respect to the stable envelope basis. This formula naturally generalizes the classical Chevalley-Monk formula…

In this paper, we obtain an explicit formula for the Chern character of a locally abelian parabolic bundle in terms of its constituent bundles. Several features and variants of parabolic structures are discussed. Parabolic bundles arising…

We characterize directs sums of twists of symmetric powers of the universal quotient bundle over the Grassmannian of lines. We use a method that could be used for analogue results on any arbitrary variety, and that should give stronger…

We consider various generalisations of the string class of a loop group bundle. The string class is the obstruction to lifting a bundle whose structure group is the loop group $LG$ to one whose structure group is the Kac-Moody central…

In this note, we give a new proof of Voisin's theorem on Green's conjecture for generic curves of odd genus resembling the first two sections of "Universal Secant Bundles and Syzygies of Canonical Curves" by the author, and so avoiding the…

We give a construction of algebraic differential characters, receiving classes of algebraic bundles with connection, lifitng the Chern-Simons invariants defined with S. Bloch, the classes in the Chow group and the analytic secondary…

Some general expressions are given for the coefficient of the 14th Chern form in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for n-dimensional differentiable…

This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae…

This is a note on MacPherson's Chern class for algebraic stacks, based on a previous paper of the author [arXiv:math/0407348]. We also discuss other additive characteristic classes in the same manner.

This is a substantial revision of the older version of this paper. The main result of the old version (the equality, up to a factor of 2 of the Beilinson and Borel regulators) is now a conjecture. The main results give equality of Beilinson…

There is an explicit formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety (in characteristic $0$) in terms of the Segre class of its jacobian subscheme; this has been known for a number of years.…

We discuss conjectures following from the attractor mechanism in type II string theory about the possible Chern classes of stable holomorphic vector bundles on Calabi-Yau threefolds. In particular, we give sufficient conditions for Chern…

Our previous papers introduce topological notions of normal crossings symplectic divisor and variety, show that they are equivalent, in a suitable sense, to the corresponding geometric notions, and establish a topological smoothability…