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Working paper

On non-Kähler degrees of complex manifolds

Angella D., Tomassini A., Verbitsky M.
We study cohomological properties of complex manifolds. In particular, we provide an upper bound for the Bott-Chern cohomology in terms of Betti numbers for compact complex surfaces, according to the dichotomy b1 even or odd. In higher dimension, a similar result is obtained at degree 1 under additional metric conditions (see Theorem 2.4).