Related papers: Noncommutative Chern form on \'etale groupoid is c…

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.

For a Lie groupoid G over a smooth manifold M we construct the adjoint action of the etale Lie groupoid G# of germs of local bisections of G on the Lie algebroid g of G. With this action, we form the associated convolution…

In the present paper we prove a statement closely related to the cyclic formality conjecture. In particular, we prove that for a divergence-free Poisson bivector field on R^d, the Kontsevich star-product with the harmonic angle function is…

In this article we construct explicit cocycles in the Alexander-Spanier cohomological complex, representing the Chern character of an element in K-theory.

We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.

We prove that twisted groupoid C*-algebras are characterised, up to isomorphism, by having Cartan semigroups, a natural generalisation of normaliser semigroups of Cartan subalgebras. This extends the classic Kumjian-Renault theory to…

We show that infinitesimal Torelli for $n$-forms holds for abelian covers of algebraic varieties of dimension $n\ge 2$, under some explicit ampleness assumptions on the building data of the cover. Moreover, we prove a variational Torelli…

We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semifinite spectral triple recovers the Connes-Moscovici cyclic…

In a series of papers, we have shown that from the representatio theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study continuous…

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 first prove the Grinberg-Kazhdan formal arc theorem without any assumptions on the characteristic. This part of the article is equivalent to arXiv:math-AG/0203263. Then we try to clarify the geometric ideas behind the proof by…

In this paper we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a riemannian \'etale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for…

We give a very simple proof that the renormalization of the Chern-Simons coupling in the Wilsonian effective action is exhausted at one-loop. Our proof can apply to arbitrary 2+1-dimensional abelian as well as nonabelian gauge theories…

We decompose the full and reduced C*-algebras of an extension of a groupoid by the circle into a direct sum of twisted groupoid C*-algebras.

We introduce the new notion of general bilinear forms (generalizing sesquilinear forms) and prove that for every ring $R$ (not necessarily commutative, possibly without involution) and every right $R$-module $M$ which is a generator (i.e.…

We describe two constructions giving rise to curved $A_{\infty}$-algebras. The first consists of deforming $A_{\infty}$-algebras, while the second involves transferring curved dg structures that are deformations of (ordinary) dg structures…

Given an $n$-gon, the poset of all collections of pairwise non-crossing diagonals is isomorphic to the face poset of some convex polytope called \textit{associahedron}. We replace in this setting the $n$-gon (viewed as a disc with $n$…

In this note, we present criteria that are equivalent to a locally compact Hausdorff groupoid $G$ being effective. One of these conditions is that $G$ satisfies the "C*-algebraic local bisection hypothesis"; that is, that every normaliser…

Let $X$ be a smooth projective variety over the complex numbers. One knows by the Cone Theorem that the closed cone of curves of $X$ is rational polyhedral whenever $c_1(X)$ is ample. For varieties $X$ such that $c_1(X)$ is not ample,…

We prove that if $V$ is a $C_2$-cofinite simple vertex operator algebra of CFT-type with a nonsingular invariant bilinear form and its an automorphism group $G$ is finite, then an orbifold model $V^G$ is also $C_2$-cofinite.