Event description
Abstract: On compact complex manifolds, the dimensions of the spaces of Dolbeault/Bott-Chern harmonic forms (the so-called Hodge numbers and Bott-Chern numbers) are independent of the choice of Hermitian metric and provide invariants of the complex structure which are often bound by topological invariants. On compact complex surfaces, the connection between Hodge numbers, Bott-Chern numbers and topological invariants is even stronger, to the point where they completely determine each other.
In this talk, we discuss the theory of harmonic forms on almost complex manifolds giving a metric-dependent generalization of Hodge and Bott-Chern numbers. On almost Kahler 4-manifolds, we show that they are actually metric-independent.