Related papers: Traces and Characteristic Classes in Infinite Dime…

For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector…

We prove an explicit formula for the total Chern character of the Verlinde bundle over the moduli space of pointed stable curves in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the…

The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in…

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…

Given a smooth action of a Lie group on a manifold, we give two constructions of the Chern character of an equivariant vector bundle in the cyclic cohomology of the crossed product algebra. The first construction associates a cycle to the…

We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We show that if X is a smooth affine scheme of dimension d over a field k of finite 2-cohomological dimension (with char(k)…

We study an invariant, the secondary trace, attached to two commuting endomorphisms of a 2-dualizable object in a symmetric monoidal higher category. We establish a secondary trace formula which encodes the natural symmetries of this…

To each second-order ordinary differential equation $\sigma $ on a smooth manifold $M$ a $G$-structure $P^\sigma $ on $J^1(\mathbb{R},M)$ is associated and the Chern connection $\nabla ^\sigma $ attached to $\sigma $ is proved to be…

We develop a theory of ``ad hoc'' Chern characters for twisted matrix factorizations associated to a scheme $X$, a line bundle ${\mathcal L}$, and a regular global section $W \in \Gamma(X, {\mathcal L})$. As an application, we establish the…

We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle $FLM\to LM$ over the loop space of a Riemannian manifold $M$. Chern-Simons forms are…

Motivic integration and MacPherson's transformation are combined in this paper to construct a theory of "stringy" Chern classes for singular varieties. These classes enjoy strong birational invariance properties, and their definition…

We introduce a new approach to traces on the principal ideal $\mathcal L_{1,\infty}$ generated by any positive compact operator whose singular value sequence is the harmonic sequence. Distinct from the well-known construction of J.~Dixmier,…

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.

Two automorphisms of a simple stable AF algebra with a finite dimensional lattice of lower semicontinuous traces are shown to be outer conjugate if they act in the same way on the K-group and the extremal traces are scaled by numbers which…

Let A be an arbitrary ring. We introduce a Dennis trace map mod n, from K_1(A;Z/n) to the Hochschild homology group with coefficients HH_1(A;Z/n). If A is the ring of integers in a number field, explicit elements of K_1(A,Z/n) are…

In this paper we give explicit formulas of differential characteristic classes of principal $G$-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes,…

R. W. Carey and J. Pincus in [CaPi86] proposed and index theory for non-Fredholm bounded operators T on a separable Hilbert space H such that TT* - T*T is in the trace class. We showed in [CGK13] using Dirac-type operators acting on…

It has been shown by Nistor that given any extension of associative algebras over C, the connecting morphism in periodic cyclic homology is compatible, under the Chern-Connes character, with the index morphism in lower algebraic K-theory.…

We study a quasimorphism, which we call the Dehn twist coefficient (DTC), from the mapping class group of a surface (with a chosen compact boundary component) that generalizes the well-studied fractional Dehn twist coefficient (FDTC) to…

In this note we clarify the relevance of ``connections up to homotopy'' to the theory of characteristic classes. We have already remarked \cite{Crai} that such connections up to homotopy can be used to compute the classical Chern…