Related papers: Sur les formules locales de l'indice
We show the presence of Poincare anomaly in Maxwell-Chern-Simons theory with an explicit mass term, in 2+1-dimensions.
We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in…
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…
Some of the developments related to quantum anomalies and path integrals during the past 10 years are briefly discussed. The covered subjects include the issues related to the local counter term in the context of 2-dimensional path integral…
The set of the first Hilbert coefficients of parameter ideals relative to a module--its Chern coefficients--over a local Noetherian ring codes for considerable information about its structure--noteworthy properties such as that of…
The second virial coefficient for non-Abelian Chern-Simons particles is recalculated. It is shown that the result is periodic in the flux parameter just as in the Abelian theory.
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where…
Taking $\mathbf{O}(D,D)$ covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative…
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae…
We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show…
We study the twisted K-theory and K-homology of some infinite dimensional spaces, like SU(\infty), in the bivariant setting. Using a general procedure due to Cuntz we construct a bivariant K-theory on the category of separable…
We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
These are the notes of a lecture given during the summer school "Geometric and Topological Methods for Quantum Field Theory", Villa de Leyva, Colombia, july 11 - 29, 2005. We review basic facts concerning gauge anomalies and discuss the…
In this paper we consider a family of Dirac-type operators on fibration $P \to B$ equivariant with respect to an action of an etale groupoid. Such a family defines an element in the bivariant $K$ theory. We compute the action of the…
In this note, we investigate the Chern classes of flat bundles in the arithmetic Deligne Cohomology, introduced by Green-Griffiths, Asakura-Saito. We show nontriviality of the Chern classes in some cases and the proof also indicates that…
In theory of topological classification, the 2D topological superconductors without time reversal symmetry are characterized by Chern numbers. However, in reality, we find the Chern numbers can not reveal the whole properties of the…
We analyse the noncommutative space underlying the quantum group SUq(2) from the spectral point of view which is the basis of noncommutative geometry, and show how the general theory developped in our joint work with H. Moscovici applies to…
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also…