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

Extensions and degenerations of spectral triples

For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's notation of quantum Gromov-Hausdorff distance between compact quantum metric spaces it is possible to define a metric on this family of spectral triples, and we show that the distance between a pair of spectral triples varies continuously with respect to the parameters. It turns out that a spectral triple associated to the unitarization of the algebra of compact operators is obtained under the limit - in this metric - for (s,1) -> (0, 1), while the basic spectral triple, associated to A, is obtained from this family under a sort of a dual limiting process for (1, t) -> (1, 0). We show that our constructions will provide families of spectral triples for the unitarized compacts and for the Podles sphere. In the case of the compacts we investigate to which extent our proposed spectral triple satisfies Connes' 7 axioms for noncommutative geometry.Comment: 40 pages. Addedd in ver. 2: Examples for the compacts and the Podle`s sphere plus comments on the relations to matricial quantum metrics. In ver.3 the word "deformations" in the original title has changed to "degenerations" and some illustrative remarks on this aspect are adde

Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry

The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply K-theory methods for the calculation of brane charges and RR-fields on hyperbolic spaces (and orbifolds thereof). It is known that by tensoring K-groups with the rationals, K-theory can be mapped to rational cohomology by means of the Chern character isomorphisms. The Chern character allows one to relate the analytic Dirac index with a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulas for Chern character, spectral invariants, and the index of a twisted Dirac operator associated with real hyperbolic spaces. Some notes for a bivariant version of topological K-theory (KK-theory) with its connection to the index of the twisted Dirac operator and twisted cohomology of hyperbolic spaces are given. Finally we concentrate on lower K-groups useful for description of torsion charges.Comment: 26 pages, no figures, LATEX. To appear in the Classical and Quantum Gravit

Demonstration of laser pulse amplification by stimulated Brillouin scattering

The energy transfer by stimulated Brillouin backscatter from a long pump pulse (15 ps) to a short seed pulse (1 ps) has been investigated in a proof-of-principle demonstration experiment. The two pulses were both amplified in different beamlines of a Nd:glass laser system, had a central wavelength of 1054 nm and a spectral bandwidth of 2 nm, and crossed each other in an underdense plasma in a counter-propagating geometry, off-set by 10∘. It is shown that the energy transfer and the wavelength of the generated Brillouin peak depend on the plasma density, the intensity of the laser pulses, and the competition between two-plasmon decay and stimulated Raman scatter instabilities. The highest obtained energy transfer from pump to probe pulse is 2.5%, at a plasma density of 0.17ncr, and this energy transfer increases significantly with plasma density. Therefore, our results suggest that much higher efficiencies can be obtained when higher densities (above 0.25ncr) are used

Target company cross-border effects in acquisitions into the UK

We analyse the abnormal returns to target shareholders in crossborder and domestic acquisitions of UK companies. The crossborder effect during the bid month is small (0.84%), although crossborder targets gain significantly more than domestic targets during the months surrounding the bid. We find no evidence for the level of abnormal returns in crossborder acquisitions to be associated with market access or exchange rate effects, and only limited support for an international diversification effect. However, the crossborder effect appears to be associated with significant payment effects, and there is no significant residual crossborder effect once various bid characteristics are controlled for

Operators, Algebras and their Invariants for Aperiodic Tilings

We review the construction of operators and algebras from tilings of Euclidean space. This is mainly motivated by physical questions, in particular after topological properties of materials. We explain how the physical notion of locality of interaction is related to the mathematical notion of pattern equivariance for tilings and how this leads naturally to the definition of tiling algebras. We give a brief introduction to the K-theory of tiling algebras and explain how the algebraic topology of K-theory gives rise to a correspondence between the topological invariants of the bulk and its boundary of a material. 1.1 Tilings and the topology of their hulls In condensed matter theory tilings are used to describe the spatial arrangement of the constitutents which make up a material, for instance a quasicrys-tal. They describe the spatial structure of the material. Associated to a tiling are various topological spaces and topological dy-namical systems. Their topology is peculiar. It takes into account the topology of the space in which the tiling lies and, at the same time, its pattern structure , that is, the way how finite patterns repeat over the tiling. Continuity in the tiling topology is related to locality in physics

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Employment and SMEs during crises

The persistent increasing duration of unemployment has become an issue during economic crises. Although lay-offs at large firms normally make headlines during crises, we still know little about the potential impact of firm size on adjustment behavior in a crisis. We studied effects of firm size on employment growth during economic slowdowns using a rich microeconomic database for the 1988-2007 period in Portuguese manufacturing industry. The results show that economic downturns affect firm growth negatively. This negative effect is found to be higher for larger firms, both during and immediately following crisis periods. Small and medium-sized enterprises (SMEs) emerge as potential stabilizers in downturn periods. However, larger firms seem to be able to quickly recover from downturn periods. Our results contribute to the scarce literature and to the understanding of the Portuguese case, where many SMEs secure most jobs. These first results may be useful, because SMEs play a determinant role in other European Union economies

Prevalence of pre-eclampsia and adverse pregnancy outcomes in women with pre-existing cardiomyopathy: a multi-centre retrospective cohort study

Pre-eclampsia is associated with postnatal cardiac dysfunction; however, the nature of this relationship remains uncertain. This multicentre retrospective cohort study aimed to determine the prevalence of pre-eclampsia in women with pre-existing cardiac dysfunction (left ventricular ejection fraction < 55%) and explore the relationship between pregnancy outcome and pre-pregnancy cardiac phenotype. In this cohort of 282 pregnancies, pre-eclampsia prevalence was not significantly increased (4.6% [95% C.I 2.2–7.0%] vs. population prevalence of 4.6% [95% C.I. 2.7–8.2], p = 0.99); 12/13 women had concurrent obstetric/medical risk factors for pre-eclampsia. The prevalence of preterm pre-eclampsia (< 37 weeks) and fetal growth restriction (FGR) was increased (1.8% vs. 0.7%, p = 0.03; 15.2% vs. 5.5%, p < 0.001, respectively). Neither systolic nor diastolic function correlated with pregnancy outcome. Antenatal ß blockers (n = 116) were associated with lower birthweight Z score (adjusted difference − 0.31 [95% C.I. − 0.61 to − 0.01], p = 0.04). To conclude, this study demonstrated a modest increase in preterm pre-eclampsia and significant increase in FGR in women with pre-existing cardiac dysfunction. Our results do not necessarily support a causal relationship between cardiac dysfunction and pre-eclampsia, especially given the population’s background risk status. The mechanism underpinning the relationship between cardiac dysfunction and FGR merits further research but could be influenced by concomitant ß blocker use