Aarhus Universitets segl

Bott-Chern cohomology and special structures in Hermitian geometry

Tommaso Sferruzza
Fredag 24. november 2023 14:15–15:15 Aud. D1 (1531-113)
Mathematics seminar

Abstract: In this seminar, I will present some recent results regarding Bott-Chern formality and its compatibility with special cohomological and metric structures in Hermitian geometry. In particular, I will focus on the interplay between the existence of strong Kähler with torsion metrics and the existence of geometrically Bott-Chern formal metrics on a class of nilmanifolds endowed with special invariant complex structures. From the cohomological point of view, I will show that, unlike the classical Massey products and the Dolbeault-Massey products, there exists an example of a compact complex manifold that satisfies the ddbar-lemma and admits a non-vanishing Aeppli-Bott-Chern-Massey product. This quite interesting result poses several questions concerning the fitting role of Bott-Chern formality in the context of homotopy theory, e.g., whether ABC-Massey products obstruct stronger cohomological conditions such as admitting a Kähler metric. I will provide a negative answer to this question for the class of Kähler solvmanifolds.

Organiseret af: CMCG
Kontakt: Giuseppe Barbaro Revideret: 21.11.2023