On the spaces of (d plus dc/-harmonic forms Hermitian manifolds and complex surfaces

In this paper, we study the spaces of (d + dc/-harmonic forms and of (d + d & fnof;/-harmonic forms, a natural generalization of the spaces of Bott-Chern harmonic forms (respectively, symplectic harmonic forms) from complex (respectively, symplectic) manifolds to almost Hermitian manifolds. We apply the same techniques to compact complex surfaces, computing their Bott-Chern and Aeppli numbers and their spaces of (d + d & fnof;/-harmonic forms. We give several applications to compact quotients of Lie groups by a lattice.