1,206 research outputs found
Euler Characteristics of Categories and Homotopy Colimits
In a previous article, we introduced notions of finiteness obstruction, Euler
characteristic, and L^2-Euler characteristic for wide classes of categories. In
this sequel, we prove the compatibility of those notions with homotopy colimits
of I-indexed categories where I is any small category admitting a finite
I-CW-model for its I-classifying space. Special cases of our Homotopy Colimit
Formula include formulas for products, homotopy pushouts, homotopy orbits, and
transport groupoids. We also apply our formulas to Haefliger complexes of
groups, which extend Bass--Serre graphs of groups to higher dimensions. In
particular, we obtain necessary conditions for developability of a finite
complex of groups from an action of a finite group on a finite category without
loops.Comment: 44 pages. This final version will appear in Documenta Mathematica.
Remark 8.23 has been improved, discussion of Grothendieck construction has
been slightly expanded at the beginning of Section 3, and a few other minor
improvements have been incoporate
Finiteness obstructions and Euler characteristics of categories
We introduce notions of finiteness obstruction, Euler characteristic,
L^2-Euler characteristic, and M\"obius inversion for wide classes of
categories. The finiteness obstruction of a category Gamma of type (FP) is a
class in the projective class group K_0(RGamma); the functorial Euler
characteristic and functorial L^2-Euler characteristic are respectively its
RGamma-rank and L^2-rank. We also extend the second author's K-theoretic
M\"obius inversion from finite categories to quasi-finite categories. Our main
example is the proper orbit category, for which these invariants are
established notions in the geometry and topology of classifying spaces for
proper group actions. Baez-Dolan's groupoid cardinality and Leinster's Euler
characteristic are special cases of the L^2-Euler characteristic. Some of
Leinster's results on M\"obius-Rota inversion are special cases of the
K-theoretic M\"obius inversion.Comment: Final version, accepted for publication in the Advances in
Mathematics. Notational change: what was called chi(Gamma) in version 1 is
now called chi(BGamma), and chi(Gamma) now signifies the sum of the
components of the functorial Euler characteristic chi_f(Gamma). Theorem 5.25
summarizes when all Euler characteristics are equal. Minor typos have been
corrected. 88 page
Topology Change in (2+1)-Dimensional Gravity
In (2+1)-dimensional general relativity, the path integral for a manifold
can be expressed in terms of a topological invariant, the Ray-Singer torsion of
a flat bundle over . 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
Toward a third generation of gravitational wave observatories
Large gravitational wave interferometric detectors, like Virgo and LIGO, demonstrated the capability to reach their design sensitivity, but to transform these machines into an effective observational instrument for gravitational wave astronomy a large improvement in sensitivity is required. Advanced detectors in the near future and third generation observatories in slightly more than one decade will open the possibility to perform gravitational wave astronomical observations from the Earth. An overview of the technological progress needed to realize a third generation observatory, like the Einstein Telescope (ET), and a possible evolution scenario are discussed in this paper
Superconductor-Ferromagnet Bi-Layers: a Comparison of s-Wave and d-Wave Order Parameters
We study superconductor-ferromagnet bi-layers, not only for s-wave but also
for d-wave superconductors. We observe oscillations of the critical temperature
when varying the thickness of the ferromagnetic layer for both s-wave and
d-wave superconductors. However, for a rotated d-wave order parameter the
critical temperature differs considerably from that for the unrotated case. In
addition we calculate the density of states for different thicknesses of the
ferromagnetic layer; the results reflect the oscillatory behaviour of the
superconducting correlations.Comment: 11 pages, 5 figures, accepted for publication in J. Phys.: Condens.
Matte
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
Optimal time-domain combination of the two calibrated output quadratures of GEO 600
GEO 600 is an interferometric gravitational wave detector with a 600 m arm-length and which uses a dual-recycled optical configuration to give enhanced sensitivity over certain frequencies in the detection band. Due to the dual-recycling, GEO 600 has two main output signals, both of which potentially contain gravitational wave signals. These two outputs are calibrated to strain using a time-domain method. In order to simplify the analysis of the GEO 600 data set, it is desirable to combine these two calibrated outputs to form a single strain signal that has optimal signal-to-noise ratio across the detection band. This paper describes a time-domain method for doing this combination. The method presented is similar to one developed for optimally combining the outputs of two colocated gravitational wave detectors. In the scheme presented in this paper, some simplifications are made to allow its implementation using time-domain methods
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
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