Twisted Dirac Operators over Quantum Spheres

We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podles quantum sphere and twisted Dirac operators.Comment: 17 page

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

C*-Algebra Extension Theory and Duality

AbstractWe develop a duality theory introduced by Paschke to give a simplified account of the main results of the Brown-Douglas-Fillmore extension theory and the relative K-homology theory of Baum and Douglas

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 experience of cognitive behavioural therapy in depressed adolescents who are fatigued

Objective: Fatigue is a common and debilitating symptom of major depressive disorder (MDD). Cognitive behavioural therapy (CBT) is a recommended psychological treatment for adolescents with moderate to severe depression. This study explored the experience of CBT in fatigued adolescents with MDD. Design: A qualitative study was conducted using existing data from the qualitative arm of a large randomized control trial, the IMPACT study. Methods: Data were obtained from semi-structured interviews conducted after therapy. Participants were 18 adolescents (aged 13–18 years) who reached the clinical threshold for fatigue on diagnostic assessment before starting treatment. The data were analysed using thematic framework analysis. Results: Three themes and seven sub-themes were developed. Adolescents appeared to find taking part in initial sessions, engaging in ongoing sessions and completing homework challenging. Perceiving the therapist as genuine seemed to provide a sense of safety which enabled adolescents to open up in sessions. When the therapist was not perceived as genuine, adolescents appeared to find CBT less helpful. The structure of CBT appeared to enable treatment goals to be set, and facilitated an increase in meaningful activity. Ensuring that tasks were perceived as manageable and goals as achievable seemed important for participation. Cognitive restructuring appeared useful, although some adolescents tended to engage in distraction from thoughts as an alternative strategy. Conclusions: This study provides an initial insight into how fatigued adolescents with MDD experience CBT. Further research is required to establish whether the themes are pervasive and relatedly, how best to treat depression in fatigued adolescents receiving CBT. Practitioner points: Fatigued adolescents with depression found engaging in CBT sessions and therapeutic homework demanding. Establishing a collaborative therapeutic relationship, where the therapist was perceived as genuine, appeared helpful for participation. The structured approach to therapy, combined with flexibility, was experienced as helpful. Adolescents who perceived the pace of sessions to be manageable and therapeutic goals as achievable seemed to find CBT helpful overall. These findings provide insight into how fatigued adolescents with depression experience CBT and highlight the importance of being aware of fatigue and adapting therapy accordingly

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

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

Motivation to study in Higher Education:a comparison between Germany and Great Britain

This article deals with reasons for the motivation to study in higher education. To find out about motives, around 200 A-level students in Germany and Great Britain were asked about their plans for the time after completion of their A-levels. Through socio-demographic data the authors could deploy facts about social backgrounds and the affiliations to socio-economic classes. There are some expected findings (e.g., British A-level students are more likely to study than their German comrades) and some pretty unexpected results (e.g., social classes do not seem to divide students into choosing university or not)