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

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

On non-formal simply connected manifolds

We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.Comment: 6 pages, Latex2

Characterization and evolution of the sediments of a Mediterranean coastal lagoon located next to a former mining area

Coastal lagoons are ecosystems that are relatively enclosed water bodies under the influence of both the terrestrial and themarine environment, being vulnerable to human impacts. Human activities, such asmining extraction, are significant anthropogenic coastal stressors that can negatively affect ecosystems and communities. In light of the above, the objective of this research is to examine the influence ofmetal mining activities on the composition of sediments of a Mediterranean coastal lagoon, named Mar Menor. This paper presents a comprehensive characterization for grain size, mineralogy, geochemistry and organic matter of sediments of this coastal lagoon, investigating their variation along space and time. Sedimentation dynamics are ruling clearly the grain size predominant in each area of the MarMenor coastal lagoon, determining the existence of entrainment, transport and sedimentation areas. Forminerals, elements and organic matter, sedimentation dynamics are also determining their distribution.The authors would like to thank Fundación Séneca for funding the project 12038/PI/09. In addition, they want to acknowledge the cooperation of J.M. Peñas, R. Baños, J. Saura, M. Saura and B. Villaescusa who helped us to improve this research and to Mr. and Mrs. Purves for their English grammar supervision

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

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