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Cohomological Aspects in Complex Non-Kähler Geometry

  • Daniele Angella

Part of the Lecture Notes in Mathematics book series (LNM, volume 2095)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Daniele Angella
    Pages 1-63
  3. Daniele Angella
    Pages 65-94
  4. Daniele Angella
    Pages 95-150
  5. Daniele Angella
    Pages 151-232
  6. Back Matter
    Pages 233-264

About this book

Introduction

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.

Keywords

32Q99, 53C55, 32Q60, 32C35, 57T15, 32G05, 32G07, 53D05, 53D18 Almost-complex structures Cohomology theories Complex manifolds Non-Kähler manifoldshl Symplectic manifolds

Authors and affiliations

  • Daniele Angella
    • 1
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02441-7
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02440-0
  • Online ISBN 978-3-319-02441-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site