Product Market Competition, Union Organizing Activity, and Employer Resistence

We develop and estimate a model of the union's optimal extent of organizing activity that accounts for the decision of employers regarding resistance to union organizing. The central exogenous variable in the analysis is the quantity of quasi-rents per worker available to be split between unions and employers. We measure available quasi-rents per worker as the difference per worker between total industry revenues net of raw materials costs and labor costs evaluated at the opportunity cost of the workers. Using two-digit industry level data for thirty-five U.S. industries for the period 1955 through 1986, we find that both organizing activity and employer resistance to unionization are positively related to available quasi-rents per worker. However, there is still a strong negative trend in union organizing activity and a strong positive trend in employer resistance after controlling for quasi-rents per worker. Thus, the explanation for the decline in union organizing activity and the increase in employer resistance to unionization since the mid 1970's lies elsewhere.

L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page

On the topological complexity of aspherical spaces

The well-known theorem of Eilenberg and Ganea expresses the Lusternik - Schnirelmann category of an aspherical space as the cohomological dimension of its fundamental group. In this paper we study a similar problem of determining algebraically the topological complexity of the Eilenberg-MacLane spaces. One of our main results states that in the case when the fundamental group is hyperbolic in the sense of Gromov the topological complexity of an aspherical space $K(\pi, 1)$ either equals or is by one larger than the cohomological dimension of $\pi\times \pi$. We approach the problem by studying essential cohomology classes, i.e. classes which can be obtained from the powers of the canonical class via coefficient homomorphisms. We describe a spectral sequence which allows to specify a full set of obstructions for a cohomology class to be essential. In the case of a hyperbolic group we establish a vanishing property of this spectral sequence which leads to the main result.Comment: 25 pages, 2 figures. This version contains an additional section 10 with Theorem

Geometric and homological finiteness in free abelian covers

We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties of regular, free abelian covers of X can be expressed in terms of the resonance varieties, extracted from the cohomology ring of X. In general, though, translated components in the characteristic varieties affect the answer. We illustrate this theory in the setting of toric complexes, as well as smooth, complex projective and quasi-projective varieties, with special emphasis on configuration spaces of Riemann surfaces and complements of hyperplane arrangements.Comment: 30 pages; to appear in Configuration Spaces: Geometry, Combinatorics and Topology (Centro De Giorgi, 2010), Edizioni della Normale, Pisa, 201

Evidence for a Bulk Complex Order-Parameter in Y0.9Ca0.1Ba2Cu3O7-delta Thin Films

We have measured the penetration depth of overdoped Y0.9Ca0.1Ba2Cu3O7-delta (Ca-YBCO) thin films using two different methods. The change of the penetration depth as a function of temperature has been measured using the parallel plate resonator (PPR), while its absolute value was obtained from a quasi-optical transmission measurements. Both sets of measurements are compatible with an order parameter of the form: Delta*dx2-y2+i*delta*dxy, with Delta=14.5 +- 1.5 meV and delta=1.8 meV, indicating a finite gap at low temperature. Below 15 K the drop of the scattering rate of uncondensed carriers becomes steeper in contrast to a flattening observed for optimally doped YBCO films. This decrease supports our results on the penetration depth temperature dependence. The findings are in agreement with tunneling measurements on similar Ca-YBCO thin films.Comment: 11 pages, 4 figure

Topology of parametrised motion planning algorithms

We introduce and study a new concept of parameterised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the parametrised setting, a motion planning algorithm has high degree of universality and flexibility, it can function under a variety of external conditions (such as positions of the obstacles etc). We explicitly compute the parameterised topological complexity of obstacle-avoiding collision-free motion of many particles (robots) in 3-dimensional space. Our results show that the parameterised topological complexity can be significantly higher than the standard (nonparametrised) invariant

Analyses of Crowd-Sourced Sound Levels of Restaurants and Bars in New York City

For several decades, there has been a significant need to better educate the public about noise pollution. A small number of small-scale studies have focused on the sound levels of restaurants and their impact on health and hearing. There have also been an increasing number of media articles stating that eating and drinking venues are getting increasingly loud making it more difficult for people to connect with others in conversation. This study reports on an exploratory large-scale noise survey of sound levels of 2,376 restaurants and bars in New York City using a novel smart-phone application and categorized them based on how quiet or loud they were. The results suggest that (1) a significant number of venues have high sound levels that are not conducive to conversation and may be endangering the health of patrons and employees (2) that the reported sound levels by the venue managers on their online public business pages generally underestimated actual sound levels, and (3) the average sound levels in restaurants and bars are correlated by neighborhood and type of cuisine