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Lorenzo Sillari

Topological invariants of almost complex 4-manifolds via harmonic forms
Thursday, 7 March, 2024 - 17:00
Résumé : 
On compact complex surfaces, the dimensions of the spaces of Dolbeault/Bott-Chern harmonic forms (the so-called Hodge/Bott-Chern numbers) are defined choosing a complex structure and a compatible Hermitian metric. It turns out that they are actually independent of both choices and are determined by the oriented topology of the underlying smooth 4-manifold.

In this talk, we discuss the theory of harmonic forms on almost complex 4-manifolds giving a metric-dependent generalization of Hodge/Bott-Chern numbers. If the metric is almost Kähler, we show that they are actually metric-independent. 

Contrarily to what happens in the complex case, some of them are determined by the oriented topology of the underlying manifold, while others are genuine almost complex invariants and allow to distinguish between different almost complex structures.
This is joint work with Adriano Tomassini.
Institution de l'orateur : 
SISSA (Trieste)
Thème de recherche : 
Salle : 
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