Algebraic structures on graph cohomology

We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in R^3.Comment: Typos corrected, exposition improved. 14 pages, 2 figures. To appear in J. Knot Theory Ramification

O Homem Espelho do Cosmo no Timeu de Platão. Os reflexos da cosmologia na formação e na constituição do homem

RESUMO Este estudo tem como objetivo geral mostrar a relação entre macrocosmo e microcosmo, especialmente em sua constituição física e psíquica. De maneira mais específica, a pesquisa pretende examinar a causa do cosmo e do homem (Demiurgo); a causa da constituição física do cosmo e do homem (Demiurgo e deuses menores); a constituição psíquica do cosmo e do homem (Alma do Mundo, alma humana e sua partição); o desequilíbrio entre cosmo e homem e suas consequências (doença, envelhecimento e morte). Para tanto, abordaremos o estudo do Timeu, o diálogo em que Platão destaca a unidade corpo-alma, sendo analisada a formação do cosmo e da Alma do Mundo em primeiro lugar (T. 29d-40d; 47e-69a) e, logo em seguida, a constituição do homem, como reflexo do cosmo (T. 40d-47e, 69a-81e) e a formação da alma humana. A fim de dar consecução ao objeto da pesquisa adotar-se-á como metodologia de estudo um procedimento monográfico ancorado em pesquisa bibliográfica. Palavras-chave: Platão. Timeu. Cosmologia. Psicologia. Fisiologia. Ética

Link Invariants of Finite Type and Perturbation Theory

The Vassiliev-Gusarov link invariants of finite type are known to be closely related to perturbation theory for Chern-Simons theory. In order to clarify the perturbative nature of such link invariants, we introduce an algebra V_infinity containing elements g_i satisfying the usual braid group relations and elements a_i satisfying g_i - g_i^{-1} = epsilon a_i, where epsilon is a formal variable that may be regarded as measuring the failure of g_i^2 to equal 1. Topologically, the elements a_i signify crossings. We show that a large class of link invariants of finite type are in one-to-one correspondence with homogeneous Markov traces on V_infinity. We sketch a possible application of link invariants of finite type to a manifestly diffeomorphism-invariant perturbation theory for quantum gravity in the loop representation.Comment: 11 page

Topological BF Theories in 3 and 4 Dimensions

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions). The vacuum expectation values of such observables give a wide range of invariants. Here we consider mainly the 3-dimensional case, where these invariants include Alexander polynomials, HOMFLY polynomials and Kontsevich integrals.Comment: 25 pages, latex, no figures. Transmission problems have been solve

4-Dimensional BF Theory as a Topological Quantum Field Theory

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that 4-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G = GL(4,R) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of 4-manifolds.Comment: 15 pages in LaTe

Determining Ratios of WIMP-Nucleon Cross Sections from Direct Dark Matter Detection Data

Weakly Interacting Massive Particles (WIMPs) are one of the leading candidates for Dark Matter. So far the usual procedure for constraining the WIMP-nucleon cross sections in direct Dark Matter detection experiments have been to fit the predicted event rate based on some model(s) of the Galactic halo and of WIMPs to experimental data. One has to assume whether the spin-independent (SI) or the spin-dependent (SD) WIMP-nucleus interaction dominates, and results of such data analyses are also expressed as functions of the as yet unknown WIMP mass. In this article, I introduce methods for extracting information on the WIMP-nucleon cross sections by considering a general combination of the SI and SD interactions. Neither prior knowledge about the local density and the velocity distribution of halo WIMPs nor about their mass is needed. Assuming that an exponential-like shape of the recoil spectrum is confirmed from experimental data, the required information are only the measured recoil energies (in low energy ranges) and the number of events in the first energy bin from two or more experiments.Comment: 33 pages, 20 eps figures; v2: typos fixed, references added and updated, revised version for publicatio

Machado de Assis e sua leitora Nise da Silveira

Nesse artigo, estaremos trabalhando com duas áreas de conhecimento: Literatura e Psicologia Junguiana. Nossa proposta é interdisciplinar: pretendemos analisar dois contos intitulados, O espelho e A causa secreta, do escritor brasileiro Machado de Assis, a partir dos trabalhos junguianos da psiquiatra brasileira Nise da Silveira

A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects

In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge group U(N), compactified on S^3 in four dimensions using Monte-Carlo techniques. The simulation is based on a particular reduction of degrees of freedom to commuting matrices of constant fields, and in particular, we can write the wave functions of these degrees of freedom exactly. The square of the wave function is equivalent to a probability density for a Boltzman gas of interacting particles in six dimensions. From the simulation we can extract the density particle distribution for each wave function, and this distribution can be interpreted as a special geometric locus in the gravitational dual. Studying the wave functions associated to half-BPS giant gravitons, we are able to show that the matrix model can measure the Planck scale directly. We also show that the output of our simulation seems to match various theoretical expectations in the large N limit and that it captures 1/N effects as statistical fluctuations of the Boltzman gas with the expected scaling. Our results suggest that this is a very promising approach to explore quantum corrections and effects in gravitational physics on AdS spaces.Comment: 40 pages, 7 figures, uses JHEP. v2: references adde

Chern-Simons States at Genus One

We present a rigorous analysis of the Schr\"{o}dinger picture quantization for the $SU(2)$ Chern-Simons theory on 3-manifold torus$\times$line, with insertions of Wilson lines. The quantum states, defined as gauge covariant holomorphic functionals of smooth $su(2)$-connections on the torus, are expressed by degree $2k$ theta-functions satisfying additional conditions. The conditions are obtained by splitting the space of semistable $su(2)$-connections into nine submanifolds and by analyzing the behavior of states at four codimension $1$ strata. We construct the Knizhnik-Zamolodchikov-Bernard connection allowing to compare the states for different complex structures of the torus and different positions of the Wilson lines. By letting two Wilson lines come together, we prove a recursion relation for the dimensions of the spaces of states which, together with the (unproven) absence of states for spins\s>{_1\over^2}level implies the Verlinde dimension formula.Comment: 33 pages, IHES/P