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

A generalized version of the TKNN-equations computing Hall conductances for generalized Dirac-like Harper operators is derived. Geometrically these equations relate Chern numbers of suitable (dual) bundles naturally associated to spectral…

We give a construction for twisted equivariant K-theory in the case of a proper action of a discrete group using twisted bundles. Our construction uses results of Lueck and Oliver to extend a construction of Adem and Ruan. We also show the…

Odd $K$-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential $K$-theory using the caloron correspondence and…

We describe polar homology groups for complex manifolds. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincare residue…

For a compact Lie group acting on a smooth manifold, we define the differential cohomology of a certain quotient stack involving principal bundles with connection. This produces differential equivariant cohomology groups that map to the…

In this note, we give a geometric expression for the multiplicities of the equivariant index of a Dirac operator twisted by a line bundle.

In this article, we define the Chern-Robinson connection on the complexify tangent bundle of an almost Robinson manifold and we study the curvature associated to. Various Bianchi identities are obtained together with an application to…

Let X be a variety over a field of characteristic 0. Given a vector bundle E on X we construct Chern forms c_{i}(E;\nabla) in \Gamma(X, \cal{A}^{2i}_{X}). Here \cal{A}^{.}_{X} is the sheaf Beilinson adeles and \nabla is an adelic…

A noncommutative-geometric generalization of classical Weil theory of characteristic classes is presented, in the conceptual framework of quantum principal bundles. A particular care is given to the case when the bundle does not admit…

In this note we show that the Chern character form of a superconnection is obtained via the parallel transport of the superconnection along superpaths, by restriction to the universal superpoint path.

Consider the blow up $\pi: \widetilde{X} \to X$ of a rational surface $X$ at a point. Let $\widetilde{V}$ be a holomorphic bundle over $\widetilde{X}$ whose restriction to the exceptional divisor equals ${\cal{O}(j) \oplus {\cal O}(-j)$ and…

We apply the concepts of superanalysis to present an intrinsically supersymmetric formulation of the Chern character in entire cyclic cohomology. We show that the cocycle condition is closely related to the invariance under…

A differential operator $D$ commuting with an $S^1$-action is said to be rigid if the non-constant Fourier coefficients of $\ker D$ and $\coker D$ are the same. Somewhat surprisingly, the study of rigid differential operators turns out to…

We show that the bivariant Chern character in entire cyclic cohomology constructed in a previous paper in terms of superconnections and heat kernel regularization, retracts on periodic cocycles under some finite summability conditions. The…

Using the construct of "Verdier specialization", we provide a purely mathematical derivation of Chern class identities which upon integration yield the D3-brane tadpole relations coming from the equivalence between F-theory and associated…

We introduce a class extending the notion of Chern-Mather class to possibly nonreduced schemes, and use it to express the difference between Schwartz-MacPherson's Chern class and the class of the virtual tangent bundle of a singular…

We show that a proper algebraic n-dimensional scheme Y admits nontrivial vector bundles of rank n, even if Y is non-projective, provided that there is a modification containing a projective Cartier divisor that intersects the exceptional…

We use invariance theory to determine the coefficient $a_{m+1,m}^{d+\delta}$ in the supertrace for the twisted de Rham complex with absolute boundary conditions.

We present combinatorial/geometric obstructions induced by the factorization over the integers of the Chern polynomial of the bundle of logarithmic vector fields associated to a complex projective plane curve. Our results generalize at the…

For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…