Related papers: Chern character and obstructions to deforming cycl…

By using higher K-theory, we reinterpret and generalize an idea on eliminating obstructions to deforming cycles, which is known to Mark Green, Phillip Griffiths and TingFai Ng(for the divisor case). As an application, we show how to…

For an ample groupoid with torsion-free stabilizers, we construct a Chern character map going from the domain of the Baum-Connes assembly map of G to the groupoid homology groups of G with rational coefficients. As a main application,…

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…

The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply…

We prove in this paper that the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of connected and simply connected Lie group, are isomorphic to the periodic cyclic homology of the quantized algebras of…

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.…

The purpose of this work is to provide details about the construction of the Chern character for categorical sheaves mentioned in our previous work "Chern character, loop spaces and derived algebraic geometry". For this, we introduce and…

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…

We consider unitary cocycle deformations of covariant $\ast$-differential calculi. We prove that complex structures, holomorphic bimodules and Chern connections on the deformed calculus are twists of their untwisted counterparts. Moreover,…

In this note we give a simple, model-independent construction of Chern classes as natural transformations from differential complex K-theory to differential integral cohomology. We verify the expected behaviour of these Chern classes with…

We define N-theory being some analogue of K-theory on the category of von Neumann algebras such that $K_0(A)\subset N_0(A)$ for any von Neumann algebra A. Moreover, it turns out to be possible to construct the extension of the Chern…

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…

In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted…

Let $X$ be a smooth complex algebraic variety and let $\operatorname{Coh} (X)$ denote its Abelian category of coherent sheaves. By the work of W. Lowen and M. Van den Bergh, it is known that the deformation theory of $\operatorname{Coh}…

We construct a quasi-inverse of the cochain map on the negative cyclic complexes of the second kind induced from the quasi-Yoneda embedding on a curved dg algebra. This gives an explicit formula for the Chern character of a perfect module.

Given a compact manifold $M$ and $g\in C^{\infty}(M,U(l;\mathbb{C}))$ we construct a Chern character $\mathrm{Ch}^-(g)$ which lives in the odd part of the equivariant (entire) cyclic Chen-normalized bar complex…

The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…

If I is a nilpotent ideal in a $\mathbb{Q}$-algebra $A$, Goodwillie defined two isomorphisms from $K_*(A,I)$ to negative cyclic homology, $HN_*(A,I)$. One is the relative version of the absolute Chern character, and the other is defined…

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and…

We establish a semistable generalization of the Beilinson-Bloch-Esnault-Kerz fiber square, relating the algebraic K-theory of a semistable scheme to its logarithmic topological cyclic homology. We prove that the obstruction to lifting…