Decomposição de grupos de dualidade de Poincaré, obstruções sing e invariantes cohomológicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um estudo sobre certos invariantes homológicos relativos duais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some remarks about Poincaré duality pairs

Bieri-Eckmann [6] introduced the concept of relative cohomology for a group pair (G, S), where G is a group and S is a family of subgroups of G and, by using that theory, they introduced the concept of Poincaré duality pairs (G, S) and provided a topological interpretation for such pairs through Eilenberg-MacLane pairs K(G, S, 1). A Poincaré duality pair is a pair (G, S) that satisfies two isomorphisms, one between absolute cohomology and relative homology and the second between relative cohomology and absolute homology. In this paper, we present a proof that those two isomorphisms are equivalent. We also present some calculations on duality pairs by using the cohomological invariant defined in [1] and studied in [2-4]. © 2012 Pushpa PublishingHouse.

Rational approximations of sectional category and Poincaré duality

Félix, Halperin, and Lemaire have shown that the rational module category Mcat and the rational Toomer invariant coincide for simply connected Poincaré duality complexes. We establish an analogue of this result for the sectional category of a fibration.

Cosmic distance duality relation and the shape of galaxy clusters

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, eta = D(L)(z)(1+ z)(2)/D(A)(z) = 1, an exact result required by the Etherington reciprocity theorem where D(L)(z) and D(A)(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D(A)(z) = D(L)(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D(A)(z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. Aims. We use WMAP (7 years) results by fixing the conventional Lambda CDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. Methods. We assume that. is a function of the redshift parametrized by two different relations: eta(z) = 1+eta(0)z, and eta(z) = 1+eta(0)z/(1+z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) beta models. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. It was found that the elliptical beta model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to eta(0) = 0 at 1 sigma), while the spherical (non-isothermal) one is only marginally compatible at 3 sigma. Conclusions. The present results derived by combining the SZE and X-ray surface brightness data from galaxy clusters with the latest WMAP results (7-years) favors the elliptical geometry for galaxy clusters. It is remarkable that a local property like the geometry of galaxy clusters might be constrained by a global argument provided by the cosmic DD relation.

Dualidade de Poincaré e invariantes cohomológicos

Pós-graduação em Matemática - IBILCE

A note about splittings of groups and commensurability under a cohomological point of view

Let G be a group, let S be a subgroup with infinite index in G and let FSG be a certain Z2G-module. In this paper, using the cohomological invariant E(G, S, FSG) or simply E˜(G, S) (defined in [2]), we analyze some results about splittings of group G over a commensurable with S subgroup which are related with the algebraic obstruction “singG(S)" defined by Kropholler and Roller ([8]. We conclude that E˜(G, S) can substitute the obstruction “singG(S)" in more general way. We also analyze splittings of groups in the case, when G and S satisfy certain duality conditions.

A dual homological invariant and some properties

Based on the cohomology theory of groups, Andrade and Fanti defined in [1] an algebraic invariant, denoted by E(G,S, M), where G is a group, S is a family of subgroups of G with infinite index and M is a Z2G-module. In this work, by using the homology theory of groups instead of cohomology theory, we define an invariant ``dual'' to E(G, S, M), which we denote by E*(G, S, M). The purpose of this paper is, through the invariant E*(G, S, M), to obtain some results and applications in the theory of duality groups and group pairs, similar to those shown in Andrade and Fanti [2], and thus, providing an alternative way to get applications and properties of this theory.

Lipopolysaccharide from Escherichia coli prevents indomethacin-induced gastric damage in rats: role of non-protein sulfhydryl groups and leukocyte adherence

To investigate the role of non-protein sulfhydryl groups (NP-SH) and leukocyte adhesion in the protective effect of lipopolysaccharide (LPS) from Escherichia coli against indomethacin-induced gastropathy. Male Wistar rats were divided into four groups: saline, LPS, saline + indomethacin and LPS + indomethacin, with six rats in each group. Rats were pretreated with LPS (300 mu g/kg, by intravenous) or saline. After 6 h, indomethacin was administered (20 mg/kg, by gavage). Three hours after treatments, rats were killed. Macroscopic gastric damage, gastric NP-SH concentration, myeloperoxidase (MPO) activity and mesenteric leukocyte adhesion (intravital microscopy) were assessed. Statistical analysis was performed using one-way analysis of variance followed by the Newman-Keuls test. Statistical significance was set at P < 0.05. LPS reduced the gastric damage, gastric MPO activity and increased gastric NP-SH concentration in indomethacin-induced gastropathy. LPS alone increased gastric NP-SH when compared to saline. Indomethacin increased leukocyte adhesion when compared to the saline, and LPS reduced indomethacin-induced leukocyte adhesion. In addition, LPS alone did not change leukocyte adhesion, when compared to the saline. LPS protective effect against indomethacin-induced gastropathy is mediated by an increase in the NP-SH and a decrease in leukocyte-endothelial adhesion.

Adsorption of aromatic compounds by activated carbon: Effects of functional groups and molecular size

The adsorption of three aromatic compounds on to an untreated carbon was investigated. The solution pH was lowered in all experiments so that all the solutes were in their molecular forms. It was shown that the difference in the maximum adsorption of the solutes was mainly a result of the difference in the sizes of the molecules and their functional groups. Further-more, it was illustrated that the packing arrangement was most likely edge-to-face (sorbate-sorbent) with various tilt angles. On the other hand, the affinity and heterogeneity of the adsorption systems were apparently related to the pK(a) values of the solutes.

Blood groups and malaria

The possible relationship between erythrocyte antigens and the presence of malaria infection by P. vivax and P. falciparurn was sought in four different ethnic groups of two departments of Colombia. Malaria infection by P. falciparum was found in 91.4% of malaria infected blacks. No significant differences were found between the presence of malaria infection and ABO antigens. In the other blood groups, it was observed that groups MNSs conferred black people a greater Rr for malaria by both species of Plasmodium and that Duffy-negative blacks and indians appeared to be resistant to P. vivax infection. A predominance of P. vivax infection was observed in Katio indians while P.falciparum was predominant in Kuna indians; the reason for this finding still needs to be explored.

Dermatophytosis: association between ABO blood groups and reactivity to the trichophytin

The authors investigated the relationship between dermatophytosis and ABO blood groups through blood typing, identification of isolated dermatophytes and specific cellular immune response of 40 individuals carriers of this mycosis. They verified that the fungus Trichophyton rubrum, isolated from 54.5% of the patients, was more frequent in individuals belonging to blood group A. The cellular immune response, evaluated through the trichophytin antigen, was positive in 25% of the studied patients; the presence of immediate reactions (30 minutes) was verified in 35%. The blood group distribution among patients with dermatophytosis and control groups was, respectively: 47.5% X 36% in group A, 40% X 50% in group O, 12.5% X 11% in group B. Even though the authors have found a higher number of patients belonging to blood group A infected by T. rubrum, these results suggest that there is no statistical evidence that these individuals are more susceptible to dermatophytosis.

The small species of Belostoma (Heteroptera, Belostomatidae): I. Key to species groups and a revision of the denticolle group

A key to species groups of the genus Belostoma Latreille, 1807, using new taxonomic characters are presented as well as the revision of the four species included in the denticolle group: B. denticolle Montandon, 1903, and three new species: B. orbiculatum from eastern Argentina and southern Brazil, B. retusum from eastern Argentina and B. amazonum from northern Brazil which are described and illustrated.

A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished infinite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

Metrics on diagram groups and uniform embeddings in a Hilbert space

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