TY  - BOOK
AU  - Angella,Daniele
ED  - SpringerLink (Online service)
TI  - Cohomological Aspects in Complex Non-Kähler Geometry
T2  - Lecture Notes in Mathematics,
SN  - 9783319024417
AV  - QA641-670 
U1  - 516.36 23
PY  - 2014///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematics
KW  - Differential equations, partial
KW  - Global differential geometry
KW  - Differential Geometry
KW  - Several Complex Variables and Analytic Spaces
N1  - Preliminaries on (almost-) complex manifolds -- Cohomology of complex manifolds -- Cohomology of nilmanifolds -- Cohomology of almost-complex manifolds -- References
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-02441-7
ER  -