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Bott-Chern Formality and Massey Products on Solvmanifolds

This is a past event.

Friday, February 16 at 11:30am to 12:30pm

DM - Deuxieme Maison, 409A
11200 SW 8th ST, Deuxieme Maison, Miami, Florida 33199

Title: Bott-Chern formality and Massey products on solvmanifolds

 

Abstract:  : Compact Kaehler manifolds and, more generally, compact complex manifolds satisfying the $\partial \overline \partial$- lemma are formal in the classical sense of Sullivan and of Dolbeault. However, for the notion of formality adapted to the Bott-Chern cohomology of a compact complex manifold, it has been shown that the (triple) Aeppli-Bott-Chern-Massey products (shortly, ABC-Massey products) do not obstruct the $\partial \overline \partial$-lemma. It is natural, then, to ask whether the existence of such products constitutes an obstruction for stronger properties, e.g., admitting a Kaehler metric.

In this talk, I will present a positive answer for the class of Kaehler solvmanifolds, by first showing a way of computing the cohomology of any Kaehler solvmanifold and then, by proving that, on such a manifold, every ABC-Massey product vanishes. Moreover, I will provide an example of a compact complex non-Kaehler manifold admitting a non vanishing quadruple ABC-Massey product, in the class of holomorphically parallelizable solvmanifolds. This is a joint work with Adriano Tomassini. 

Event Type

Academics, Lectures & conferences

Audience

Students, Faculty & Staff, Alumni

Tags

GEOMETRY AND TOPOLOGY

Department
Department of Mathematics and Statistics
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