Smoothness of the future and past trapped sets in Kerr-Newman-Taub-NUT spacetimes

We consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that, from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

An overview of the gravitational spin Hall effect

In General Relativity, the propagation of electromagnetic waves is usually described by the vacuum Maxwell's equations on a fixed curved background. In the limit of infinitely high frequencies, electromagnetic waves can be localized as point particles, following null geodesics. However, at finite frequencies, electromagnetic waves can no longer be treated as point particles following null geodesics, and the spin angular momentum of light comes into play, via the spin-curvature coupling. We will refer to this effect as the gravitational spin Hall effect of light. Here, we review a series of theoretical results related to the gravitational spin Hall effect of light, and we compare the predictions of different models. The analogy with the spin Hall effect in Optics is also explored, since in this field the effect is well understood, both theoretically and experimentally

Symplectic cohomology and q-intersection numbers

Given a symplectic cohomology class of degree 1, we define the notion of an equivariant Lagrangian submanifold. The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces a grading by generalized eigenspaces. Taking Euler characteristics with respect to the induced grading yields a deformation of the intersection number. Dehn twists act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz fibrations give fully computable examples. A key step in computations is to impose the "dilation" condition stipulating that the BV operator applied to the symplectic cohomology class gives the identity. Equivariant Lagrangians mirror equivariant objects of the derived category of coherent sheaves.Comment: 32 pages, 9 figures, expanded introduction, added details of example 7.5, added discussion of sign

Contact orderability up to conjugation

We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of non-compact contact manifolds, called convex at infinity.Comment: 28 pages, 1 figur

Échange international et distorsions internes:Comment gouverner la globalisation ?

La concurrence des pays émergents de la taille de la Chine ou de l’Inde fait resurgir avec force le débat qui oppose partisans et adversaires du libre-échange au sein même des pays développés. Pour les premiers, la croissance du commerce international est forcément bénéficiaire pour tous. Pour les seconds, elle est la cause de tous les maux et en particulier du chômage. Les choses sont pourtant bien différentes et beaucoup moins simples. Les changements dans le commerce international, comme d’ailleurs le progrès technique, créent inévitablement des distorsions qui perturbent le fonctionnement de l’économie. Ces distorsions ne sont pas réductibles à des dysfonctionnements des marchés des biens ou du travail. Elles ne peuvent donc pas être éliminées ab initio en choisissant des institutions optimales. Pour autant, des restrictions au commerce international ne sont pas une solution car elles risquent de créer d’autres distorsions qui viennent s’ajouter aux premières. Des distorsions avant tout intérieures appellent des solutions intérieures. Pour explorer ces solutions, il faut retenir une analyse conçue pour étudier, non les propriétés des positions d’équilibre avant et après l’ouverture à l’échange, mais les caractéristiques d’un processus de transition dont le succès n’est pas assuré. Ce type d’analyse permet de mettre en évidence la nécessité d’introduire une forme d’inertie dans les mécanismes d’ajustement. Si une relative flexibilité des salaires est encore possible quand l’intensité du changement est limitée, une certaine viscosité est requise dans le cas contraire, et un accès facilité aux ressources financières externes est nécessaire. Ce résultat pourrait aider à formuler les choix institutionnels et organisationnels à mettre en œuvre dans les économies qui veulent tirer avantage du commerce international et de la globalisation.Changes in the pattern of international trade inevitably create distortions that perturb the functioning of the economy. These distortions may not be reduced to malfunctioning goods or labour markets, and hence cannot be eliminated by simply choosing the optimal institutions. Domestic distortions call for domestic solutions. To explore these solutions it is useless to analyze the properties of equilibria before and after the opening to trade. Rather, we need to build an analytical framework suited to investigate the characteristics of a transition process whose success is not guaranteed ex ante. it appears that wage rigidity and an easy access to external financial resources are necessary in presence of fast pace of change, while if change is sufficiently slow the standard recipe of wage flexibility may be appropriate. These results may help in the institutional and organizational choices to be implemented in economies willing to profit from international trade and globalization

Nanosize Titanium Dioxide Stimulates Reactive Oxygen Species in Brain Microglia and Damages Neurons in Vitro

BackgroundTitanium dioxide is a widely used nanomaterial whose photo-reactivity suggests that it could damage biological targets (e.g., brain) through oxidative stress (OS).ObjectivesBrain cultures of immortalized mouse microglia (BV2), rat dopaminergic (DA) neurons (N27), and primary cultures of embryonic rat striatum, were exposed to Degussa P25, a commercially available TiO2 nanomaterial. Physical properties of P25 were measured under conditions that paralleled biological measures.FindingsP25 rapidly aggregated in physiological buffer (800–1,900 nm; 25°C) and exposure media (~ 330 nm; 37°C), and maintained a negative zeta potential in both buffer (–12.2 ± 1.6 mV) and media (–9.1 ± 1.2 mV). BV2 microglia exposed to P25 (2.5–120 ppm) responded with an immediate and prolonged release of reactive oxygen species (ROS). Hoechst nuclear stain was reduced after 24-hr (≥100 ppm) and 48-hr (≥2.5 ppm) exposure. Microarray analysis on P25-exposed BV2 microglia indicated up-regulation of inflammatory, apoptotic, and cell cycling pathways and down-regulation of energy metabolism. P25 (2.5–120 ppm) stimulated increases of intracellular ATP and caspase 3/7 activity in isolated N27 neurons (24–48 hr) but did not produce cytotoxicity after 72-hr exposure. Primary cultures of rat striatum exposed to P25 (5 ppm) showed a reduction of immunohistochemically stained neurons and microscopic evidence of neuronal apoptosis after 6-hr exposure. These findings indicate that P25 stimulates ROS in BV2 microglia and is nontoxic to isolated N27 neurons. However, P25 rapidly damages neurons at low concentrations in complex brain cultures, plausibly though microglial generated ROS