Uniform version of Weyl-von Neumann theorem

We prove a "quantified" version of the Weyl-von Neumann theorem, more precisely, we estimate the ranks of approximants to compact operators appearing in the Voiculescu's theorem applied to commutative algebras. This allows considerable simplifications in uniform K-homology theory, namely it shows that one can represent all the uniform K-homology classes on a fixed Hilbert space with a fixed *-representation of C_0(X), for a large class of spaces X

Noncommutative geometry, topology and the standard model vacuum

As a ramification of a motivational discussion for previous joint work, in which equations of motion for the finite spectral action of the Standard Model were derived, we provide a new analysis of the results of the calculations herein, switching from the perspective of Spectral triple to that of Fredholm module and thus from the analogy with Riemannian geometry to the pre-metrical structure of the Noncommutative geometry. Using a suggested Noncommutative version of Morse theory together with algebraic $K$-theory to analyse the vacuum solutions, the first two summands of the algebra for the finite triple of the Standard Model arise up to Morita equivalence. We also demonstrate a new vacuum solution whose features are compatible with the physical mass matrix.Comment: 24 page

Invariant expectations and vanishing of bounded cohomology for exact groups

We study exactness of groups and establish a characterization of exact groups in terms of the existence of a continuous linear operator, called an invariant expectation, whose properties make it a weak counterpart of an invariant mean on a group. We apply this operator to show that exactness of a finitely generated group $G$ implies the vanishing of the bounded cohomology of $G$ with coefficients in a new class of modules, which are defined using the Hopf algebra structure of $\ell_1(G)$.Comment: Final version, to appear in the Journal of Topology and Analysi

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Satisfaction with knowledge and competencies:a multi-country study of employers and business graduates

This study critically discusses findings from a research project involving four European countries. The project had two main aims. The first was to develop a systematic procedure for assessing the balance between knowledge and competencies acquired in higher, further and vocational education and the specific needs of the labor market. The second aim was to develop and test a set of meta-level quality indicators aimed at evaluating the linkages between education and employment. The project was designed to address the lack of employer input concerning the requirements of business graduates for successful workplace performance and the need for more specific industry-driven feedback to guide administrative heads at universities and personnel at quality assurance agencies in curriculum development and revision. Approach: The project was distinctive in that it combined different partners from higher education, vocational training, industry and quality assurance. Project partners designed and implemented an innovative approach, based on literature review, qualitative interviews and surveys in the four countries, in order to identify and confirm key knowledge and competency requirements. This study presents this step-by-step approach, as well as survey findings from a sample of 900 business graduates and employers. In addition, it introduces two Partial Least Squares (PLS) path models for predicting satisfaction with work performance and satisfaction with business education. Results: Survey findings revealed that employers were not very confident regarding business graduates’ abilities in key knowledge areas and in key generic competencies. In subsequent analysis, these graduate abilities were tested and identified as important predictors of employers’ satisfaction with graduates’ work performance. Conclusion: The industry-driven approach introduced in this study can serve as a guide to assist different types of educational institutions to better align study programs with changing labor market requirements. Recommendations for curriculum improvement are discussed

KO-Homology and Type I String Theory

We study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology. We define an analytic version of KO-homology using KK-theory of real C*-algebras, and construct explicitly the isomorphism between geometric and analytic KO-homology. The construction involves recasting the Cl(n)-index theorem and a certain geometric invariant into a homological framework which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas. We show that this invariant also naturally assigns torsion charges to non-BPS states in Type I string theory, in the construction of classes of D-branes in terms of topological KO-cycles. The formalism naturally captures the coupling of Ramond-Ramond fields to background D-branes which cancel global anomalies in the string theory path integral. We show that this is related to a physical interpretation of bivariant KK-theory in terms of decay processes on spacetime-filling branes. We also provide a construction of the holonomies of Ramond-Ramond fields in Type II string theory in terms of topological K-chains.Comment: 40 pages; v4: Clarifying comments added, more detailed proof of main isomorphism theorem given; Final version to be published in Reviews in Mathematical Physic

Elliptic operators on manifolds with singularities and K-homology

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.Comment: revised version; 25 pages; section with applications expande

D-branes, KK-theory and duality on noncommutative spaces

We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology, a refinement of open string T-duality, and a general criterion for cancellation of global worldsheet anomalies

The K-theoretic Farrell-Jones Conjecture for hyperbolic groups

We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.Comment: 33 pages; final version; to appear in Invent. Mat

Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame cases. The algebra of row-column-finite (or locally finite) matrices over an arbitrary field is one of the algebras considered in this paper, its representation type is shown to be finite.Comment: 33 page