Related papers: Atiyah covering index theorem for riemannian folia…

We define an $L^2$-signature for proper actions on spaces of leaves of transversely oriented foliations with bounded geometry. This is achieved by using the Connes fibration to reduce the problem to the case of Riemannian bifoliations where…

We introduce the concepts of branched coarse coverings and transfers between coarse homology theories along them. We show that various versions of coarse $K$-homology theories admit the additional structure of transfers. We show versions of…

We give applications of the higher Lefschetz theorems for foliations of [BH10], primarily involving Haefliger cohomology. These results show that the transverse structures of foliations carry important topological and geometric information.…

We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann--Roch theorem.

The $L^2$-Index Theorem of Atiyah \cite{atiyah} expresses the index of an elliptic operator on a closed manifold $M$ in terms of the $G$-equivariant index of some regular covering $\widetilde{M}$ of $M$, with $G$ the group of covering…

This paper is motivated by Deninger's programme. First we prove, using Alvarez Lopez-Kordyukov results, an Atiyah-Bott-Lefschetz trace formula for the cohomology groups associated to a ramified leafwise flat line bundle on a riemannian…

We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator $D_m$ on the maximal Connes-Skandalis Hilbert module and…

Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifold M, with compact quotient. There is an assembly map which associates to any G-equivariant K-homology class on M, an element of the…

In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with…

We give a uniform construction of the higher indices of elliptic operators associated to Alexander-Spanier cocycles of either parity in terms of a pairing a la Connes between the K-theory and the cyclic cohomology of the algebra of complete…

For an orbifold X and $\alpha \in H^3(X, Z)$, we introduce the twisted cohomology $H^*_c(X, \alpha)$ and prove that the Connes-Chern character establishes an isomorphism between the twisted K-groups $K_\alpha^* (X) \otimes C$ and twisted…

We generalize the decomposition theorem of Hochschild, Kostant and Rosenberg for Hochschild (co-)homology to arbitrary morphisms between complex spaces or schemes over a field of characteristic zero. To be precise, we show that for each…

This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of…

We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codimension one foliations. Since the twisting of the commutators turns the…

Molino's theory is a mathematical tool for studying Riemannian foliations. In this paper, we propose a generalization of Molino's theory with two Riemannian foliations. For this purpose, the projection of foliation with respect to a…

We give a cohomological formula for the index of a fully elliptic pseudodifferential operator on a manifold with boundary. As in the classic case of Atiyah-Singer, we use an embedding into an euclidean space to express the index as the…

We prove an Atiyah-Segal isomorphism for the higher $K$-theory of coherent sheaves on quotient Deligne-Mumford stacks over $\C$. As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an…

Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral…

We investigate the homological ideal $\mathfrak{J}_G^H$, the kernel of the restriction functors in compact Lie group equivariant Kasparov categories. Applying the relative homological algebra developed by Meyer and Nest, we relate the…

We study differential operators on complete Riemannian manifolds which act on sections of a bundle of finite type modules over a von Neumann algebra with a trace. We prove a relative index and a Callias-type index theorems for von Neumann…