Related papers: Quasihomomorphisms and the residue Chern character
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…
In previous work we generalised both the odd and even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of…
In this note some generalization of the Chern character is discussed from the chromatic point of view. We construct a multiplicative G_{n+1}-equivariant natural transformation \Theta from some height (n+1) cohomology theory E^*(-) to the…
We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological…
We show a quantum version of Chern character homomorphism from the small quantum K-theory to the small quantum cohomology in the cases of projective spaces and incidence varieties, whose classical limit gives the classical Chern character…
These notes form the next episode in a series of articles dedicated to a detailed proof of a cohomological index formula for transversally elliptic pseudo-differential operators and applications. The first two chapters are already available…
In this paper we construct a bivariant Chern character defined on ``families of spectral triples''. Such families should be viewed as a version of unbounded Kasparov bimodules adapted to the category of bornological algebras. The Chern…
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.…
This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework…
We present a higher index theorem for a certain class of etale one-dimensional complex-analytic groupoids. The novelty is the use of the local anomaly formula established in a previous paper, which represents the bivariant Chern character…
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…
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…
We obtain a precise relation between the Chern-Schwartz-MacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of…
The Chern character of a complex vector bundle is most conveniently defined as the exponential of a curvature of a connection. It is well known that its cohomology class does not depend on the particular connection chosen. It has been shown…
We prove the multiplicative property of localized Chern characters. As a direct consequence, a localized Chern character gives rise to a ring homomorphism from the K-group of periodic complexes to the bivariant Chow cohomology group. As an…
Let G be a finite group, and let E be a generalised cohomology theory, subject to certain technical conditions. We study a certain ring C(E,G) that is the best possible approximation to E^0BG that can be built using only knowledge of the…
We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the…
For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete K\"ahler metric of Fefferman. We compute the conformal anomaly in complex dimension two and apply…
This short note establishes a relationship between a generalized version of the Radul residue cocycle introduced in former works of the author and the Connes-Moscovici residue cocycle, and discusses the applicability of such a formula to…
Conical zeta values associated with rational convex polyhedral cones generalise multiple zeta values. We renormalise conical zeta values at poles by means of a generalisation of Connes and Kreimer's Algebraic Birkhoff Factorisation. This…