Related papers: The character map in deformation quantization

For a smooth finite cyclic covering over a projective space of dimension greater than one, we show that the group of automorphisms acts faithfully on the cohomology except for a few cases. In characteristic zero, we study the equivariant…

Cheeger-Simons differential characters, Deligne cohomology in the smooth category, the Hopkins-Singer construction of ordinary differential cohomology and the recent Harvey-Lawson constructions are each in two distinct ways Abelian group…

Let $A$ be a finite-dimensional smooth unital cyclic $A_\infty$-algebra. Assume furthermore that $A$ satisfies the Hodge-to-de-Rham degeneration property. In this short note, we prove the non-commutative analogue of the…

We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…

We extend the Chern character on K-theory, in its generalization to the Chern-Dold character on generalized cohomology theories, further to (twisted, differential) non-abelian cohomology theories, where its target is a non-abelian de Rham…

The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild…

We prove a conjecture raised by Tsygan, namely the existence of an L-infinity-quasiisomorphism of L-infinity-modules between the cyclic chain complex of smooth functions on a manifold and the differential forms on that manifold. Concretely,…

We generalize Kontsevich's construction of L-infinity derivations of polyvector fields from the affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph…

We conjecture an explicit formula for a cyclic analog of the Formality $L_{\infty}$-morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg map, is in fact a morphism (and a quasiisomorphism) of the…

First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation…

In this paper we prove, with details and in full generality, that the isomorphism induced on tangent homology by the Shoikhet-Tsygan formality $L_\infty$-quasi-isomorphism for Hochschild chains is compatible with cap-products. This is a…

We introduce a version of the Cartier isomorphism for de Rham cohomology valid for associative, not necessarily commutative algebras over a field of positive characteristic. Using this, we imitate the well-known argument of P. Deligne and…

We prove that, for every compact Kaehler manifold, the period map of its Kuranishi family is induced by a natural L-infinity morphism. This implies, by standard facts about L-infinity algebras, that the period map is a "morphism of…

A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a…

In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed `Herman map' is developed.…

We consider the 2-cocycle deformation of algebras graded by discrete groups. The action of the Maurer-Cartan form on cyclic cohomology is shown to be cohomologous to the cup product action of the group cocycle. This allows us to compute the…

Using Chern character, we construct a natural transformation from the local Hilbert functor to a functor of Artin rings defined from Hochschild homology, which allows us to reconstruct the semi-regularity map and the infinitesimal…

We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class…

In this paper, we construct and study derived character maps of finite-dimensional representations of $\infty$-groups. As models for $\infty$-groups we take homotopy simplicial groups, i.e. homotopy simplicial algebras over the algebraic…

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…