Cohomological Aspects in Complex Non-Kähler Geometry

Daniele Angella

ISBN 10: 331902440X / ISBN 13: 9783319024400

Published by Springer International Publishing, Springer International Publishing Dez 2013, 2013

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure.On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler 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 Kähler 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 292 pp. Englisch.

Seller Inventory # 9783319024400

Bibliographic Details

• Title: Cohomological Aspects in Complex Non-Kähler Geometry
• Publisher: Springer International Publishing, Springer International Publishing Dez 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 331902440X
• ISBN 13: 9783319024400
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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

On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler 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 Kähler 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.