Related papers: Connes trace theorem for Carnot manifolds

In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the…

We examine the ranks of operators in semi-finite C*-algebras as measured by their densely defined lower semicontinuous traces. We first prove that a unital simple C*-algebra whose extreme tracial boundary is nonempty and finite contains…

We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with…

The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and…

This paper is a sequel to our earlier work [BFPRW], where we study the derived representation scheme DRep_{g}(A) parametrizing the representations of a Lie algebra A in a finite-dimensional reductive Lie algebra g. In [BFPRW], we defined…

It is shown that the pairing of the K00 group of a C*-algebra with the densely defined traces of the algebra can be extended to a pairing with the densely defined weights. For traces the pairing can be extended to the K0 group without the…

Gauge fields have a natural metric interpretation in terms of horizontal distance. The latest, also called Carnot-Caratheodory or subriemannian distance, is by definition the length of the shortest horizontal path between points, that is to…

We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group $R^l$. Under deformation by a torus action, a standard formula…

We study the relationships between Dixmier traces, zeta-functions and traces of heat semigroups beyond the dual of the Macaev ideal and in the general context of semifinite von Neumann algebras. We show that the correct framework for this…

In a previous paper ([1]), we associated a holonomy groupoid and a C*-algebra to any singular foliation (M,F). Using these, we construct the associated pseudodifferential calculus. This calculus gives meaning to a Laplace operator of any…

A trace $\tau$ on a separable C*-algebra $A$ is called matricial field (MF) if there is a trace-preserving morphism from $A$ to $Q_\omega$, where $Q_\omega$ denotes the norm ultrapower of the universal UHF-algebra $Q$. In general, the trace…

Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols. We…

We construct an analogue of Kontsevich and Vishik's canonical trace for a class of pseudodifferential boundary value problems in Boutet de Monvel's calculus on compact manifolds with boundary. For an operator A in the calculus (of class…

We establish a compensated compactness theorem in the microlocal and geometric analytic framework. For a weakly $L^2_{\rm loc}$-convergent sequence of sections of a vector bundle over a semi-Riemannian manifold whose image under a…

We compute the K-theory of the C*-category generated by order zero, equivariant, properly supported, classical pseudodifferential operators acting on sections of homogeneous bundles over the symmetric space of a real reductive Lie group G.…

First-order differential operators arising from the representation-theoretic decomposition of the covariant derivative play a central role in Riemannian geometry. In this paper, we study Stein-Weiss $O(n)$-gradients acting on covariant…

We establish several analogues of the classical Lidskii Theorem for some special classes of singular traces (Dixmier traces and Connes-Dixmier traces) used in noncommutative geometry.

We study properties of the boundary trace operator on the Sobolev space $W^1_1(\Omega)$. Using the density result by Koskela and Zhang, we define a surjective operator \mbox{$Tr: W^1_1(\Omega_K)\rightarrow X(\Omega_K)$}, where $\Omega_K$ is…

We introduce a new canonical trace on odd class logarithmic pseudo-differential operators on an odd dimensional manifold, which vanishes on commutators. When restricted to the algebra of odd class classical pseudo-differential operators our…

In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defined, and trace and lifting results with respect to a…