On linear combinations of cohomological invariants of compact complex manifolds

We prove that there are no unexpected universal integral linear relations and congruences between Hodge, Betti Chern numbers of compact complex manifolds determine the combinations such which bimeromorphic or topological invariants. This extends results in Kähler case by Kotschick Schreieder. then develop a framework to tackle more general questions taking into account ‘all’ cohomological invariants (e.g. dimensions higher pages Frölicher spectral sequence, Bott-Chern Aeppli cohomology). allows us reduce specific construction problems. solve these problems many cases. In particular, we obtain full answers concerning low dimensions.