Moduli Spaces and Formal Operads

Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus g with n marked points. With the operations which relate the different moduli spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a modular operad of projective smooth Deligne-Mumford stacks, overline{M}. In this paper we prove that the modular operad of singular chains C_*(overline{M};Q) is formal; so it is weakly equivalent to the modular operad of its homology H_*(overline{M};Q). As a consequence, the "up to homotopy" algebras of these two operads are the same. To obtain this result we prove a formality theorem for operads analogous to Deligne-Griffiths-Morgan-Sullivan formality theorem, the existence of minimal models of modular operads, and a characterization of formality for operads which shows that formality is independent of the ground field.Comment: 36 pages (v3: some typographical corrections

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence between its localization with respect to weak equivalences and the localised category of cofibrant objets with respect to strong equivalences. This equivalence allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and functor categories with a triple, in the last case we find examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications, we prove the existence of filtered minimal models for \emph{cdg} algebras over a zero-characteristic field and we formulate an acyclic models theorem for non additive functors

Probing the interaction between solid benzene and water using vacuum ultraviolet and infrared spectroscopy

We present results of a combined vacuum ultravioloet (VUV) and infrared (IR) photoabsorption study of amorphous benzene:water mixtures and layers to investigate the benzene-water interaction in the solid phase. UV spectra of 1:1, 1:10 and 1:100 benzene:water mixtures at 24 K reveal a concentration dependent shift in the energies of the 1B2u, 1B1u and 1E1u electronic states of benzene. All the electronic bands blueshift from pure amorphous benzene towards gas phase energies with increasing water concentration. IR results reveal a strong dOH-π benzene-water interaction via the dangling OH stretch of water with the delocalised π system of the benzene molecule. Although this interaction influences the electronic states of benzene with the benzenewater interaction causing a redshift in the electronic states from that of the free benzene molecule, the benzene-benzene interaction has a more significant effect on the electronic states of benzene. VUV spectra of benzene and water layers show evidence of non-wetting between benzene and water, characterised by Rayleigh scattering tails at wavelengths greater than 220 nm. Our results also show evidence of benzene-water interaction at the benzene-water interface affecting both the benzene and the water electronic states. Annealing the mixtures and layers of benzene and water show that benzene remains trapped within in/under water ice until water desorption near 160 K. These first systematic studies of binary amorphous mixtures in the VUV, supported with complementary IR studies, provide a deeper insight into the influence of intermolecular interactions on intramolecular electronic states with significant implications for our understanding of photochemical processes in more realistic astrochemical environments

Distribución biogeográfica de las hormigas (Hymenoptera, Formicidae) en las Islas del Mediterráneo Occidental

Abstract not availabl

A Conformal Mapping and Isothermal Perfect Fluid Model

Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as ``minimally'' curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three parameter family of perfect fluid solution which is static and inhomogeneous. The density and pressure fall off in the curvature radial coordinates as $R^{-2},$ for unbounded cosmological model with a barotropic equation of state. This is the characteristic of isothermal fluid. We thus have an ansatz for isothermal perfect fluid model. The solution can also represent bounded fluid spheres.Comment: 10 pages, TeX versio

On the theory of diamagnetism in granular superconductors

We study a highly disordered network of superconducting granules linked by weak Josephson junctions in magnetic field and develop a mean field theory for this problem. The diamagnetic response to a slow {\it variations} of magnetic field is found to be analogous to the response of a type-II superconductor with extremely strong pinning. We calculate an effective penetration depth $\lambda_g$ and critical current $j_c$ and find that both $\lambda_g^{-1}$ and $j_c$ are non-zero but are strongly suppressed by frustration.Comment: REVTEX, 12 pages, two Postscript figure