On Thom spaces, Massey products and non-formal symplectic manifolds

In this work we analyze the behavior of Massey products of closed manifolds under the blow-up construction. The results obtained in the article are applied to the problem of constructing closed symplectic non-formal manifolds. The proofs use Thom spaces as an important technical tool. This application of Thom spaces is of conceptual interest.Comment: 16 pages, amstex, changes according to the referee suggestions. accepted by IMR

Simply-connected K-contact and Sasakian manifolds of dimension 7

We construct a compact simply-connected 7-dimensional manifold admitting a K-contact structure but not a Sasakian structure. We also study rational homotopy properties of such manifolds, proving in particular that a simply-connected 7-dimensional Sasakian manifold has vanishing cup-product on the second cohomology and that it is formal if and only if all its triple Massey products vanish.Comment: 14 pages, some references added, several typos are correcte

Generalized symplectic symmetric spaces

Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask a question about their possible symplectic versions. We do construct such generalizations and extend some of Bieliavsky's results. In particular, we classify all 3-symmetric symplectic spaces

On the algebraic independence of Hamiltonian characteristic classes

We prove that Hamiltonian characteristic classes defined as fibre integrals of powers of the coupling class are algebraically independent for generic coadjoint orbits.Comment: 9 pages, no figure