Alexander Invariants of Complex Hyperplane Arrangements

Let A be an arrangement of complex hyperplanes. The fundamental group of the complement of A is determined by a braid monodromy homomorphism from a finitely generated free group to the pure braid group. Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of A. From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of A. We also provide a combinatorial criterion for when these lower bounds are attained.Comment: 26 pages; LaTeX2e with amscd, amssymb package

The boundary manifold of a complex line arrangement

We study the topology of the boundary manifold of a line arrangement in CP^2, with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial Delta(G), and more generally, the twisted Alexander polynomial associated to the abelianization of G and an arbitrary complex representation. We give an explicit description of the unit ball in the Alexander norm, and use it to analyze certain Bieri-Neumann-Strebel invariants of G. From the Alexander polynomial, we also obtain a complete description of the first characteristic variety of G. Comparing this with the corresponding resonance variety of the cohomology ring of G enables us to characterize those arrangements for which the boundary manifold is formal.Comment: This is the version published by Geometry & Topology Monographs on 22 February 200

Characteristic varieties of arrangements

The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex algebraic n-torus. In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of V_k(A). For any arrangement A, we show that the tangent cone at the identity of this variety coincides with R^1_k(A), one of the cohomology support loci of the Orlik-Solomon algebra. Using work of Arapura and Libgober, we conclude that all positive-dimensional components of V_k(A) are combinatorially determined, and that R^1_k(A) is the union of a subspace arrangement in C^n, thereby resolving a conjecture of Falk. We use these results to study the reflection arrangements associated to monomial groups.Comment: LaTeX2e, 20 pages. A reference to Libgober's recent work in math.AG/9801070 is added. Several points are clarified, a new example is include

Torsion in Milnor fiber homology

In a recent paper, Dimca and Nemethi pose the problem of finding a homogeneous polynomial f such that the homology of the complement of the hypersurface defined by f is torsion-free, but the homology of the Milnor fiber of f has torsion. We prove that this is indeed possible, and show by construction that, for each prime p, there is a polynomial with p-torsion in the homology of the Milnor fiber. The techniques make use of properties of characteristic varieties of hyperplane arrangements.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-16.abs.htm

Challenges of Internet of Things and Big Data Integration

The Internet of Things anticipates the conjunction of physical gadgets to the In-ternet and their access to wireless sensor data which makes it expedient to restrain the physical world. Big Data convergence has put multifarious new opportunities ahead of business ventures to get into a new market or enhance their operations in the current market. considering the existing techniques and technologies, it is probably safe to say that the best solution is to use big data tools to provide an analytical solution to the Internet of Things. Based on the current technology deployment and adoption trends, it is envisioned that the Internet of Things is the technology of the future, while to-day's real-world devices can provide real and valuable analytics, and people in the real world use many IoT devices. Despite all the advertisements that companies offer in connection with the Internet of Things, you as a liable consumer, have the right to be suspicious about IoT advertise-ments. The primary question is: What is the promise of the Internet of things con-cerning reality and what are the prospects for the future.Comment: Proceedings of the International Conference on International Conference on Emerging Technologies in Computing 2018 (iCETiC '18), 23rd -24th August, 2018, at London Metropolitan University, London, UK, Published by Springer-Verla

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Los Acuerdos Comerciales Globales y Profundos De La Unión Europea Y El Sistema Multilateral Del Comercio

This contribution undertakes a review of the terms of the debate on the interaction of the EU's deep and comprehensive trade agreements with the multilateral trade system, in order to point out the absence of analysis models to evaluate the effects of the agreements promoting deep integration. The study further examines the economic and systemic ramifications of preferential agreements to assess whether EU agreements pose a threat to the multilateral trading system or if they could contribute to reinvigorate multilateral negotiations.La presente contribución emprende una revisión de los términos en los que se sustancia el debate sobre la interacción de los acuerdos comerciales globales y profundos de la UE con el sistema multilateral del comercio, con vistas a destacar la ausencia de modelos de análisis para valorar el impacto de los acuerdos que promueven una integración profunda de los mercados. Además, el estudio aborda los efectos económicos y sistémicos de los acuerdos preferenciales, a fin de determinar si los acuerdos de la UE constituyen una amenaza para el sistema multilateral o, si pueden contribuir a revitalizar las negociaciones multilaterales

Single-Cell Tests to Explore the Reliability of Sofc Installations Operating Offshore

This paper studies the robustness of off-shore solid oxide fuel cell (SOFC) installations and the nature and causes of possible cell degradation in marine environments. Two important, cathode-related, impediments to ensuring SOFC reliability in off-shore installations are: cathode degradation due to salt contamination and oxygen depletion in the air supply. Short-term and long-term tests show the effect of salt contamination in the cathode feed on cell performance, and reveal the underlying cause of the degradation seen. SEM/X-ray Diffraction/(XRD) analyses made it possible to identify salt taken up in the cathode microstructure after the short-term testing while the macroscopic cell structure remained intact after the short-term tests. The long-term degradation was found to be more severe, and SEM images showed delamination at the cathode/electrolyte interface with salt present, something that was not seen after long-term testing without salt. The effect of oxygen depletion on the performance was also determined at three different temperatures using I-V curves.publishedVersio