The Ore condition, affiliated operators, and the lamplighter group

Let G be the wreath product of Z and Z/2, the so called lamplighter group and k a commutative ring. We show that kG does not have a classical ring of quotients (i.e. does not satisfy the Ore condition). This answers a Kourovka notebook problem. Assume that kG is contained in a ring R in which the element 1-x is invertible, with x a generator of Z considered as subset of G. Then R is not flat over kG. If k is the field of complex numbers, this applies in particular to the algebra UG of unbounded operators affiliated to the group von Neumann algebra of G. We present two proofs of these results. The second one is due to Warren Dicks, who, having seen our argument, found a much simpler and more elementary proof, which at the same time yielded a more general result than we had originally proved. Nevertheless, we present both proofs here, in the hope that the original arguments might be of use in some other context not yet known to us.Comment: LaTex2e, 7 pages. Added a new proof of the main result (due to Warren Dicks) which is shorter, easier and more elementary, and at the same time yields a slightly more general result. Additionally: misprints removed. to appear in Proceedings of "Higher dimensional manifold theory", Conference at ICTP Trieste 200

Topology Change in (2+1)-Dimensional Gravity

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial topology change are nonvanishing---in fact, they can be infrared divergent---but that they are infinitely suppressed relative to similar topology-preserving amplitudes.Comment: 19 pages of text plus 4 pages of figures, LaTeX (using epsf), UCD-11-9

Experimental verification of a zero-dimensional model of the ionization kinetics of XeCl discharges

An improved 0-dimensional model for XeCl high-pressure glow discharges is presented. Calculated discharge voltages are compared with precise measurements at a small, very homogeneous discharge. Excellent agreement in a wide parameter field demonstrates that this model may serve as a reference for simpler models describing the ionization kinetics

Analysis of a four-mirror cavity enhanced Michelson interferometer

We investigate the shot noise limited sensitivity of a four-mirror cavity enhanced Michelson interferometer. The intention of this interferometer topology is the reduction of thermal lensing and the impact of the interferometers contrast although transmissive optics are used with high circulating powers. The analytical expressions describing the light fields and the frequency response are derived. Although the parameter space has 11 dimensions, a detailed analysis of the resonance feature gives boundary conditions allowing systematic parameter studies

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

The universal functorial equivariant Lefschetz invariant

We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K_0 of the category of "phi-endomorphisms of finitely generated free RPi(G,X)-modules". We derive results about fixed points of equivariant endomorphisms of cocompact proper smooth G-manifolds.Comment: 33 pages; shortened version of the author's PhD thesis, supervised by Wolfgang Lueck, Westfaelische Wilhelms-Universitaet Muenster, 200

Small volume coaxial discharge as precision testbed for 0D-models of XeCl lasers

In order to check the predictions of 0D-models experimentally, a small coaxial discharge configuration for the generation of homogeneous high pressure glow discharges (diameter 11 mm, length 20 mm) in rare gas halogen excimer laser gas mixtures under accurately controlled conditions has been developed. It uses X-ray preionization and a special pulse-forming network (PFN) delivering fast rising (8 ns) single square pulses (U 0=25 kV; I=300 A; prop=100 ns). Discharge current and voltage are measured precisely by a capacitive voltage divider and a shunt integrated into the discharge chamber. All circuit data needed for the model calculations have been evaluated. Interferometric and spectroscopic diagnostics of the bulk of the discharge and of the cathode sheath have been performed. First results for Ne/Xe/HCl mixtures are compared with model calculations

Complement activated granulocytes can cause autologous tissue destruction in man

Activation of polymorphonuclear granulocytes (PMNs) by C5a is thought to be important in the pathogenesis of multiple organ failure during sepsis and after trauma. In our experiment exposure of human PMNs to autologous zymosan activated plasma (ZAP) leads to a rapid increase in chemiluminescence. Heating the ZAP at 56°C for 30 min did not alter the changes, while untreated plasma induced only baseline activity. The respiratory burst could be completely abolished by decomplementation and preincubation with rabbit antihuman C5a antibodies. Observation of human omentum using electron microscopy showed intravascular aggregation of PMNs, with capillary thrombosis and diapedesis of the cells through endothelial junctions 90 s after exposure to ZAP. PMNs caused disruption of connections between the mesothelial cells. After 4 min the mesothelium was completely destroyed, and connective tissue and fat cells exposed. Native plasma and minimum essential medium did not induce any morphological changes. These data support the concept that C5a activated PMNs can cause endothelial and mesothelial damage in man. Even though a causal relationship between anaphylatoxins and organ failure cannot be proved by these experiments C5a seems to be an important mediator in the pathogenesis of changes induced by severe sepsis and trauma in man