An 8-dimensional non-formal simply connected symplectic manifold

A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.Comment: 8 pages, 1 figure; v2. exposition greatly improved; v3. final version. To appear in Annals of Mathematic

Formality of Donaldson submanifolds

We introduce the concept of s-formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n-1), is formal if and only if M is (n-1)-formal. The formality and the hard Lefschetz property are studied for the symplectic manifolds constructed by Donaldson with asymptotically holomorphic techniques. This study permits us to show an example of a Donaldson symplectic manifold of dimension eight which is formal simply connected and does not satisfy the hard Lefschetz theorem.Comment: 24 pages, no figures, Latex2e; v3. statement of Lemma 2.7 correcte

Non-formal co-symplectic manifolds

We study the formality of the mapping torus of an orientation-preserving diffeomorphism of a manifold. In particular, we give conditions under which a mapping torus has a non-zero Massey product. As an application we prove that there are non-formal compact co-symplectic manifolds of dimension $m$ and with first Betti number $b$ if and only if $m=3$ and $b \geq 2$, or $m \geq 5$ and $b \geq 1$. Explicit examples for each one of these cases are given.Comment: Only minor changes with respect to version 1 (some terminology clarified). 21 pages, no figures. To appear in Trans. Am. Math. So

Formality and the Lefschetz property in symplectic and cosymplectic geometry

We review topological properties of K\"ahler and symplectic manifolds, and of their odd-dimensional counterparts, coK\"ahler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the K\"ahler/symplectic situation) and the $b_1=1$ case (in the coK\"ahler/cosymplectic situation).Comment: 27 pages, no figures. Comments are welcome

On formality of Sasakian manifolds

We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using this we produce a method of constructing simply connected K-contact non-Sasakian manifolds. On the other hand, for every $n \geq 3$, we exhibit the first examples of simply connected compact Sasakian manifolds of dimension $2n + 1$ which are non-formal. They are non-formal because they have a non-zero triple Massey product. We also prove that arithmetic lattices in some simple Lie groups cannot be the fundamental group of a compact Sasakian manifold.Comment: 22 pages, no figures; v2. some corrections; v3. Accepted in J. Topolog

La historiografía filosófica argentina, una lectura desde la obra de Macedonio Fernández

La historiografía filosófica en la Argentina comienza a organizarse de un modo sistemático entre fines del siglo XIX y primeras décadas del siglo XX. Este proceso corre paralelo a la institucionalización del saber filosófico en las universidades. La filosofía como disciplina irá adquiriendo autonomía al mismo tiempo que un paulatino desentendimiento respecto de lo social, cuyos efectos se harán evidentes en la despolitización de la misma. En este sentido, la lectura de la obra del escritor-pensador argentino Macedonio Fernández es especialmente fecunda para interpelar algunos de los límites sobre los que se ha organizado la historiografía filosófica.Philosophical historiography begins in Argentina to be systematically organized between the end of the 19th century and the first decades of the 20th.This process runs parallel to the institutionalization of philosophical studies in the university. Philosophy as a discipline acquired autonomy while, at the same time, steadily ignoring social aspects. The evident effects of this resulted in a loss of political awareness. In this sense, reading the work of Argentinean writer-thinker Macedonio Fernández is particularly fruitful when interpreting some of the limits within which philosophical historiography has been organized.Fil: Muñoz, Marisa Alejandra. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Ciencias Humanas, Sociales y Ambientales; Argentin

Quiroga, Hugo; Villavicencio, Susana; Vermeren, Patrice (comp.). Filosofías de la ciudadanía. Sujeto político y democracia. Rosario (Argentina), Homo Sapiens Ediciones, 1999, 260p.

Fil: Muñoz, Marisa Alejandra