Related papers: Twisted Cyclic Cohomology and Modular Fredholm Mod…
We construct Fredholm modules over an algebra taking values in generalized Hilbert spaces over a rigid $C^*$-tensor category. Using methods of Connes, we obtain Chern characters taking values in cyclic cohomology. These Chern characters are…
We replace a ring with a small $\mathbb C$-linear category $\mathcal{C}$, seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the…
It is shown that Connes' character formula for unbounded, theta-summable Fredholm modules represents the abstract Chern-character in K-homology. As an application, the character of a particular Fredholm module over the reduced group…
In this paper, we continue our program of systematic categorification of the Noncommutative Differential Geometry of Connes. We replace a ring with a small $\mathbb C$-linear category, seen as a ring with several objects in the sense of…
We give a survey of cyclic homology/cohomology theory including a detailed discussion of cyclic theories for various classes of topological algebras. We show how to associate cyclic classes with Fredholm modules and $K$-theory classes and…
We derive simple explicit formulas for the character of a cycle in the Connes' (b,B)-bicomplex of cyclic cohomology and give applications to the Fredholm modules and equivariant characteristic classes.
We introduce the notion of a {\vartheta}-summable Fredholm module over a locally convex dg algebra {\Omega} and construct its Chern character as a cocycle on the entire cyclic complex of {\Omega}, extending the construction of Jaffe,…
Let $\Omega$ be a locally convex differential graded algebra. We introduce the Chern character of $\vartheta$-summable $\mathcal{C}_q$-Fredholm modules over $\Omega$, generalizing the JLO cocycle to the differential graded setting. This…
We prove excision in entire and periodic cyclic cohomology and construct a Chern-Connes character for Fredholm modules over a C*-algebra without summability restrictions, taking values in a variant of Connes's entire cyclic cohomology.…
We propose a definition of a modular spectral triple which covers existing examples arising from KMS-states, Podles sphere and quantum SU(2). The definition also incorporates the notion of twisted commutators appearing in recent work of…
We show that the (even and odd) index cocycles for theta-summable Fredholm modules are in the image of the Connes-Moscovici characteristic map. To show this, we first define a new range of asymptotic cohomologies, and then we extend the…
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 examine Hopf cyclic cohomology in the same context as the analysis of the geometry of loop spaces $LX$ in derived algebraic geometry and the resulting close relationship between $S^1$-equivariant quasi-coherent sheaves on $LX$ and…
To each algebra over the complex numbers we associate a sequence of abelian groups in a contravariant functorial way. In degree (m-1) we have the m-summable Fredholm modules over the algebra modulo stable m-summable perturbations. These new…
We construct a family of odd, finitely summable Fredholm modules over the crossed product C*-algebra $C(\bd \G)\rtimes \G$ associated to the action of a non-elementary hyperbolic group $\G$ on its Gromov boundary $\bd \G$. These Fredholm…
The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which…
We consider cycles for graded $C^{*,r}$-algebras (Real $C^{*}$-algebras) which are compatible with the $*$-structure and the real structure. Their characters are cyclic cocycles. We define a Connes type pairing between such characters and…
The purpose of this paper is to apply the framework of non- commutative differential geometry to quantum deformations of a class of Kahler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm…
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…
Certain cocycles constructed by Connes are characters of $p$-summable Fredholm modules. In this article, we establish some consequences of the universal properties which these characters enjoy. Our main technical result is that the entire…