## Cohomological Aspects in Complex Non-Kähler Geometry by Daniele Angella

By Daniele Angella

In those notes, we offer a precis of contemporary effects at the cohomological homes of compact advanced manifolds now not endowed with a Kähler structure.

On the single hand, the massive variety of constructed analytic innovations makes it attainable to end up robust cohomological houses for compact Kähler manifolds. at the different, on the way to extra examine any of those homes, it really is typical to seem for manifolds that don't have any Kähler structure.

We concentration particularly on learning Bott-Chern and Aeppli cohomologies of compact complicated manifolds. numerous effects about the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, permitting readers to review particular examples. Manifolds endowed with almost-complex buildings, or with different specific buildings (such as, for instance, symplectic, generalized-complex, etc.), also are considered.