Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Topological and geometric consequences of the almost Kähler identities

I will explain a generalization of the so-called "Kähler identities" to the non-integrable setting. Among these are identities of various Laplacians, dualities à la Hodge, Serre and hard Lefschetz, as well as a Lefschetz-type decomposition theorem on certain spaces of harmonic forms. I will then explain some topological implications of these identities involving Betti numbers and the fundamental group of a compact almost Kähler manifold. In particular, I will present new combined geometric/topological obstructions for a manifold to admit a symplectic form compatible with a given almost complex structure.