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Cohomological aspects in complex non-Kähler geometry / Daniele Angella.

By: Angella, Daniele [author.]Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2095.Publisher: Cham : Springer, 2014Description: 1 online resource (xxv, 262 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783319024417; 3319024418Subject(s): Complex manifolds | Cohomology operations | Geometry, Differential | Cohomology operations | Complex manifolds | Geometry, DifferentialGenre/Form: Electronic books. Additional physical formats: Print version:: Cohomological aspects in complex non-Kähler geometry.DDC classification: 515/.946 LOC classification: QA331Online resources: Click here to access online
Contents:
Preliminaries on (almost- ) complex manifolds -- Cohomology of complex manifolds -- Cohomology of nilmanifolds -- Cohomology of almost-complex manifolds.
Summary: In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kahler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kahler 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 Kahler 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.
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Preliminaries on (almost- ) complex manifolds -- Cohomology of complex manifolds -- Cohomology of nilmanifolds -- Cohomology of almost-complex manifolds.

Includes bibliographical references and index.

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kahler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kahler 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 Kahler 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.

Online resource; title from PDF title page (SpringerLink, viewed November 25, 2013).

English.

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