On non-K\"ahler degrees of complex manifolds
  We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman, which provides an upper bound for the Bott-Chern cohomology in terms of Betti numbers for compact complex surfaces according to the dichotomy $b_1$ even or odd. 
Daniele Angella, Adriano Tomassini, Misha Verbitsky
math.DG math.CV