On the spaces of $(d+d^c)$-harmonic forms and $(d+d^{\Lambda })$-harmonic forms on almost Hermitian manifolds and complex surfaces

Abstract

We study the spaces of $(d+d^c)$-harmonic forms and $(d+d^{\Lambda })$-harmonic forms, the natural generalization of the spaces of Bott-Chern harmonic forms, resp. symplectic harmonic forms from complex, resp. symplectic, manifolds to almost Hermitian manifolds. With the same techniques, we also prove that Bott-Chern and Aeppli numbers of compact complex surfaces depend only on the topology of the underlying manifold, a fact that was well-known for Hodge numbers of compact complex surfaces. We give several applications to compact quotients of Lie groups by a lattice.

26 pages, no figures. V2: updated attribution and references of Theorem C. Updated bibliography. Version submitted for publication. Comments are welcome

Cited by in corpus (1)

• Invariant and non-invariant almost complex structures on compact quotients of Lie groups