Topology of four-manifolds with special homotopy groups

We study the homotopy type and thes—cobordism class of a closed connected topological 4-manifold with vanishing second homotopy group. Our results are related to problem 4.53 of Kirby inGeometric Topology, Studies in Advanced Math.2(1997), and give a partial answer to a question stated by Hillman inBull. London Math. Soc.27(1995) 387–391

A note on irreducible Heegaard diagrams

AbstractWe construct a Heegaard diagram of genus three for the real projective 3-space, which has no waves and pairs of complementary handles. The first example was given by Im and Kim but our diagram has smaller complexity. Furthermore the proof presented here is quite different to that of the quoted authors, and permits also to obtain a simple alternative proof of their result. Examples of irreducible Heegaard diagrams of certain connected sums complete the paper.We construct a Heegaard diagram of genus three for the real projective 3-space, which has no waves and pairs of complementary handles. The first example was given by Im and Kim but our diagram has smaller complexity. Furthermore the proof presented here is quite different to that of the quoted authors, and permits also to obtain a simple alternative proof of their result. Examples of irreducible Heegaard diagrams of certain connected sums complete the paper

On graph-theoretical invariants of combinatorial manifolds

The goal of this paper is to give some theorems which relate to the problem of classifying combinatorial (resp. smooth) closed manifolds up to piecewise-linear (PL) homeomorphism. For this, we use the combinatorial approach to the topology of PL manifolds by means of a special kind of edge--colored graphs, called {sl crystallizations}. Within this representation theory, Bracho and Montejano introduced in 1987 a nonnegative numerical invariant, called the reduced complexity, for any closed n-dimensional PL manifold. Here we consider this invariant, and extend in this context the concept of average order first introduced by Luo and Stong in 1993, and successively investigated by Tamura in 1996 and 1998. Then we obtain some classification results for closed connected smooth low-dimensional manifolds according to reduced complexity and average order. Finally, we answer to a question posed by Trout in 2013

Recognizing Euclidean Space Forms with Minimal Fundamental Tetrahedra

We completely recognize the topological structure of the ten compact euclidean space forms with special minimal tetrahedra, constructed by face pairings in nice papers of Molnár [8-9]. From these polyhedral descriptions we derive special presentations with two generators for the fundamental groups of the considered manifolds. Our proofs also show that such group presentations completely characterize the euclidean space forms among closed connected $3$-manifolds. The results have also didactical importance

A splitting theorem for homotopy equivalent smooth 4-manifolds

We prove a decomposition theorem for closed connected homotopy equivalent smooth four-manifolds, which partially extends a recent result of Curtis et al. (1996) to the non-simply connected case. Then we study the question of when a homotopy equivalence between closed smooth 4-manifolds is homotopic to a topological homeomorphism. In particular, we obtain a new proof of the well-known uniqueness of closed aspherical smooth 4-manifolds with good fundamental groups

An efficient and versatile synthesis of new Trojan-horse cephalosporins

A useful synthesis of new dual-action cephalosporins is reported. These molecules could represent a fascinating tool for treatment of bacterial infectious diseases, since they display a possible inhibitor activity towards beta-lactamase-expressing bacteria. The major advantage of this 3-step synthetic approach lies in its versatility, which allows the systematic preparation of a wide pool of new molecules

Fundamental Group and Covering Properties of Hyperbolic Surgery Manifolds

We study a family of closed connected orientable 3-manifolds obtained by Dehn surgeries with rational coefficients along the oriented components of certain links. This family contains all the manifolds obtained by surgery along the (hyperbolic) 2-bridge knots. We find geometric presentations for the fundamental group of such manifolds and represent them as branched covering spaces. As a consequence, we prove that the surgery manifolds, arising from the hyperbolic 2-bridge knots, have Heegaard genus 2 and are 2-fold coverings of the 3-sphere branched over well-specified links

Families of group presentations related to topology

AbstractWe study some algebraic properties of a class of group presentations depending on a finite number of integer parameters. This class contains many well-known groups which are interesting from a topological point of view. We find arithmetic conditions on the parameters under which the considered groups cannot be fundamental groups of hyperbolic 3-manifolds of finite volume. Then we investigate the asphericity for many presentations contained in our family

Cavitating pulmonary nodules growing in a favourable medium

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QUANDO OS CAMPOS SÃO A CIDADE: O ESPAÇO URBANO EM JOGO NAS TRAMAS DO FUTEBOL DE VÁRZEA

O presente artigo problematiza a urbanização de São Paulo (SP) na chave do processo de uso e apropriação do espaço, com enfoque no futebol popular e nos campos de várzea. No primeiro momento, o debate é dedicado à emergência do futebol na capital paulista e o modo como emergiram, nos bairros populares, arranjos que deram origem às centenas de campos que se espraiaram pela cidade, cuja posterior rarefação está ligada à concepção de espaço-mercadoria no âmbito das políticas urbanas. Em seguida, o artigo direciona a discussão para duas instâncias de uso do espaço, mediadas pela administração pública, onde tensões, agenciamentos, permanências e rupturas perpassam os espaços varzeanos, destacando como crianças e jovens apreendem a cidade a partir do futebol. Palavras-chave: Futebol de várzea; Espaço; São Paulo.   When the fields are the city: the urban space at stake in the plots of lowland football Abstract: The present article problematizes the urbanization of São Paulo (SP) in terms of the process of use and appropriation of space, with a focus on football fields. At first, the debate is devoted to the emergence of footbal l in the city and the way in which arrangements emerged in popular neighborhoods that gave rise to the hundreds of fields that spread across the city, but whose subsequent rarefaction is linked to the concept of space commodity. within the scope of urban p olicies. Then, the article directs the discussion to two instances of space use, media ted by the public administration, where tensions, agency, permanence and ruptures permeate the sports spaces, highlighting how children and young people apprehend the cit y from football. Keywords: Amateur Football Space São Paulo.   Cuando los campos son la ciudad: el espacio urbano en juego en las parcelas del fútbol llano Resumen: El presente artículo problematiza la urbanización de São Paulo (SP) en términos del proceso de uso y apropiación del espacio, con foco en las canchas de fútbol. En un primer momento, el debate está dedicado a la eclosión del fútbol en la ciudad y la forma en que surgieron los arreglos en los barrios populares que dieron origen a los campos que se repartieron por la ciudad, pero cuyo posterior enrarecimiento está ligado al concepto de espacio-mercancía en el ámbito de las políticas urbanas. Luego, el artículo analiza dos instancias de uso del espacio, mediadas por la administración pública, donde tensiones, agencias, permanencias y rupturas permean los espacios populares, destacando cómo niños y jóvenes aprehenden la ciudad desde el fútbol. Palabras clave: Fútbol; Espacio; São Paulo