Cohomological Aspects in Complex Non-Kähler Geometry

By Daniele Angella

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a K?hler structure.

On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact K?hler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any K?hler structure.

We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.

• Format: Paperback
• Language: English
• ISBN: 331902440X
• ISBN13: 9783319024400
• Release Date: December 2013
• Publisher: Springer
• Length: 262 Pages
• Weight: 0.91 lbs.
• Dimensions: 0.6" x 6.1" x 9.2"