Cohomological Aspects on Complex and Symplectic Manifolds

  • Nicoletta TardiniEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 21)


We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent useful tools in studying non Kähler geometry. We give an overview on the comparisons among the dimensions of the cohomology groups that can be defined and we show how we reach the \(\partial \overline{\partial }\)-lemma in complex geometry and the Hard-Lefschetz condition in symplectic geometry. For more details we refer to Angella and Tardini (Proc Am Math Soc 145(1):273–285, 2017) and Tardini and Tomassini (Int J Math 27(12), 1650103 (20 pp.), 2016).



The author would like to thank the organizers Daniele Angella, Paolo de Bartolomeis, Costantino Medori and Adriano Tomassini for the kind invitation to the INdAM Meeting Complex and Symplectic Geometry held at Palazzone of Cortona. Many thanks to all the participants at the conference who contributed to create such a nice environment. Special thanks also to Adriano Tomassini and Daniele Angella for their constant support, encouragement, for many useful discussions on the subject and for their contribution to the results obtained jointly with the author. This proceeding is dedicated to the memory of the very kind person and excellent mathematician Paolo de Bartolomeis.

The project is partially supported by the GNSAGA of INdAM.


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Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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