Related papers: Asymptotic Morphisms and Elliptic Operators over C…

Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${{KK}}_e(C,A)^{++}$ the set of those $\kappa$ for which…

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method…

We give a simple proof of the cobordism invariance of the index of an elliptic operator. The proof is based on a study of a Witten-type deformation of an extension of the operator to a complete Riemannian manifold. One of the advantages of…

The Atiyah-Singer index theorem is a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the principal symbol of the operator. On contact…

We generalize Roe's Index Theorem for operators of Dirac type on open manifolds to elliptic pseudodifferential operators. To this end we introduce a class of pseudodifferential operators on manifolds of bounded geometry which is more…

We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the…

In math.QA/0311303 B. Feigin, G. Felder, and B. Shoikhet proposed an explicit formula for the trace density map from the quantum algebra of functions on an arbitrary symplectic manifold M to the top degree cohomology of M. They also…

These notes are based on lectures on index theory, topology, and operator algebras at the "School on High Dimensional Manifold Theory" at the ICTP in Trieste, and at the Seminari di Geometria 2002 in Bologna. We describe how techniques…

Motivated by the Fredholm theory on the standard Hilbert module over an unital C*-algebra introduced by Mishchenko and Fomenko, we provide a new approach to axiomatic Fredholm theory in unital C*-algebras established by Keckic and Lazovic…

Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups, or equivalently, for certain reduced partial crossed products. In the case of…

We prove an abstract theorem of maximal hypoellipticy showing that in an abstract calculus under some natural assumptions, an operator is maximally hypoelliptic if and only if its principal symbol is left invertible. We then show that our…

A generalization of Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^*$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology and the…

Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac…

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.…

In previous definition of $\mathrm{E}$-theory, separability of the $\mathrm{C}^*$-algebras is needed either to construct the composition product or to prove the long exact sequences. Considering the latter, the potential failure of the long…

In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay,…

We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings…

In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…

We study the C*-closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with non-empty boundary. We find short exact sequences in K-theory…

In this paper we deal with a second order multidimensional fractional differential operator. We consider a case where the leading term represented by the uniformly elliptic operator and the final term is the Kipriyanov operator of…